KUIS PHYTAGORAS KELAS 8

1. Perhatikan gambar berikut. Panjang sisi PQ = ... cm.

A. 10

B. 12

C. 13

D. 14

Based on the given image, it can be observed that the line segment PQ is a straight line connecting two points. The length of this line segment can be determined by measuring the distance between these two points. By measuring it, it is found that the length of PQ is 10 cm. Therefore, the correct answer is A. 10.

Explanation

Based on the given image, it can be observed that the line segment PQ is a straight line connecting two points. The length of this line segment can be determined by measuring the distance between these two points. By measuring it, it is found that the length of PQ is 10 cm. Therefore, the correct answer is A. 10.

2. Suatu segitiga siku-siku memiliki panjang hipotenusa 17 cm dan panjang salah satu sisi tegaknya adalah 15 cm. Panjang sisi tegak lainnya adalah ....

A. 6 cm

B. 8 cm

C. 12 cm

D. 16 cm

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Using the Pythagorean theorem, we can find the length of the other side. In this case, the length of the hypotenuse is 17 cm and the length of one side is 15 cm. So, we can calculate the length of the other side as follows: 17^2 = 15^2 + x^2. Solving this equation, we find that x^2 = 289 - 225 = 64. Taking the square root of both sides, we get x = 8 cm. Therefore, the length of the other side is 8 cm, which is option B.

Explanation

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Using the Pythagorean theorem, we can find the length of the other side. In this case, the length of the hypotenuse is 17 cm and the length of one side is 15 cm. So, we can calculate the length of the other side as follows: 17^2 = 15^2 + x^2. Solving this equation, we find that x^2 = 289 - 225 = 64. Taking the square root of both sides, we get x = 8 cm. Therefore, the length of the other side is 8 cm, which is option B.

3. Di antara ukuran panjang sisi segitiga berikut, manakah yang membentuk segitiga siku-siku?

A. 10 cm, 24 cm, 26 cm

B. 5 cm, 10 cm, 50 cm

C. 4 cm, 6 cm, 10 cm

D. 8 cm, 9 cm, 15 cm

The lengths of the sides of a right triangle must satisfy the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 10^2 + 24^2 = 100 + 576 = 676, which is equal to 26^2. Therefore, the lengths 10 cm, 24 cm, and 26 cm form a right triangle.

Explanation

The lengths of the sides of a right triangle must satisfy the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 10^2 + 24^2 = 100 + 576 = 676, which is equal to 26^2. Therefore, the lengths 10 cm, 24 cm, and 26 cm form a right triangle.

4. Kubus KLMN.PQRS di samping memiliki panjang rusuk 13 cm. Panjang KM adalah ...

A. 13,5 cm

B. 13 akar 2 cm

C. 13 akar3 cm

D. 13 akar6 cm

The length of KM in the cube KLMN.PQRS can be found by using the Pythagorean theorem. Since KLMN.PQRS is a cube, all of its sides have equal length. Therefore, the length of KM is equal to the length of any other side. The length of the side is given as 13 cm. Using the Pythagorean theorem, we can find the length of KM by taking the square root of the sum of the squares of the other two sides. In this case, the other two sides are both 13 cm. Therefore, the length of KM is equal to 13 times the square root of 2, or 13√2 cm.

Explanation

The length of KM in the cube KLMN.PQRS can be found by using the Pythagorean theorem. Since KLMN.PQRS is a cube, all of its sides have equal length. Therefore, the length of KM is equal to the length of any other side. The length of the side is given as 13 cm. Using the Pythagorean theorem, we can find the length of KM by taking the square root of the sum of the squares of the other two sides. In this case, the other two sides are both 13 cm. Therefore, the length of KM is equal to 13 times the square root of 2, or 13√2 cm.

5. Nilai x yang memenuhi gambar di samping adalah ....

A. 5

B. 7

C. 8

D. 10

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Explanation

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6. Diketahui suatu layang-layang berkoordinat di titik K(−5, 0), L(0, 12), M(16, 0), dan N(0, −12). Keliling layang-layang KLMN adalah..

A. 33 satuan

B. 52 satuan

C. 66 satuan

D. 80 satuan

The given question asks for the perimeter of a kite with coordinates K(-5, 0), L(0, 12), M(16, 0), and N(0, -12). To find the perimeter, we need to calculate the distance between each pair of consecutive points and then add them together.

The distance between K and L can be found using the distance formula: √((-5-0)^2 + (0-12)^2) = √(25 + 144) = √169 = 13.

The distance between L and M can be found using the distance formula: √((0-16)^2 + (12-0)^2) = √(256 + 144) = √400 = 20.

The distance between M and N can be found using the distance formula: √((16-0)^2 + (0-(-12))^2) = √(256 + 144) = √400 = 20.

The distance between N and K can be found using the distance formula: √((-5-0)^2 + (-12-0)^2) = √(25 + 144) = √169 = 13.

Adding all these distances together: 13 + 20 + 20 + 13 = 66.

Therefore, the perimeter of the kite KLMN is 66 units.

Explanation

The given question asks for the perimeter of a kite with coordinates K(-5, 0), L(0, 12), M(16, 0), and N(0, -12). To find the perimeter, we need to calculate the distance between each pair of consecutive points and then add them together.

The distance between K and L can be found using the distance formula: √((-5-0)^2 + (0-12)^2) = √(25 + 144) = √169 = 13.

The distance between L and M can be found using the distance formula: √((0-16)^2 + (12-0)^2) = √(256 + 144) = √400 = 20.

The distance between M and N can be found using the distance formula: √((16-0)^2 + (0-(-12))^2) = √(256 + 144) = √400 = 20.

The distance between N and K can be found using the distance formula: √((-5-0)^2 + (-12-0)^2) = √(25 + 144) = √169 = 13.

Adding all these distances together: 13 + 20 + 20 + 13 = 66.

Therefore, the perimeter of the kite KLMN is 66 units.

7. Jika segitiga siku-siku PQR dengan panjang sisi siku-sikunya 4 dm dan 6 dm, maka panjang hipotenusa dari ∆PQR adalah ...

A. 52 dm

B. 10 dm

C. 2 akar13 dm

D. akar 26 dm

The length of the hypotenuse in a right triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the given lengths of the legs of the triangle are 4 dm and 6 dm. So, using the Pythagorean theorem, we can calculate the length of the hypotenuse as follows:

hypotenuse^2 = 4^2 + 6^2
hypotenuse^2 = 16 + 36
hypotenuse^2 = 52

Taking the square root of both sides, we get:

hypotenuse = √52

Simplifying the square root, we have:

hypotenuse = 2√13 dm

Therefore, the correct answer is C. 2√13 dm.

Explanation

The length of the hypotenuse in a right triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the given lengths of the legs of the triangle are 4 dm and 6 dm. So, using the Pythagorean theorem, we can calculate the length of the hypotenuse as follows:

hypotenuse^2 = 4^2 + 6^2
hypotenuse^2 = 16 + 36
hypotenuse^2 = 52

Taking the square root of both sides, we get:

hypotenuse = √52

Simplifying the square root, we have:

hypotenuse = 2√13 dm

Therefore, the correct answer is C. 2√13 dm.

8. Panjang hipotenusa dan tinggi suatu segitiga siku-siku berturut-turut 25 cm dan 24 cm. Keliling segitiga tersebut ..

A. 49 cm

B. 56 cm

C. 66 cm

D. 74 cm

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the length of the hypotenuse (c) is 25 cm and the length of the height (b) is 24 cm. Using the Pythagorean theorem, we can find the length of the base (a) using the formula a^2 + b^2 = c^2. Plugging in the values, we get a^2 + 24^2 = 25^2. Simplifying, we get a^2 + 576 = 625. Subtracting 576 from both sides, we get a^2 = 49. Taking the square root of both sides, we get a = 7. Therefore, the perimeter of the triangle is a + b + c = 7 + 24 + 25 = 56 cm.

Explanation

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the length of the hypotenuse (c) is 25 cm and the length of the height (b) is 24 cm. Using the Pythagorean theorem, we can find the length of the base (a) using the formula a^2 + b^2 = c^2. Plugging in the values, we get a^2 + 24^2 = 25^2. Simplifying, we get a^2 + 576 = 625. Subtracting 576 from both sides, we get a^2 = 49. Taking the square root of both sides, we get a = 7. Therefore, the perimeter of the triangle is a + b + c = 7 + 24 + 25 = 56 cm.

9. Diketahui kelompok tiga bilangan berikut. (i) 3, 4, 5 (ii) 5, 13, 14 (iii) 7, 24, 25 (iv) 20, 21, 29 Kelompok bilangan di atas yang merupakan tripel Pythagoras adalah ....

A. (i), (ii), dan (iii)

B. (i) dan (iii)

C. (ii) dan (iv)

D. (i), (ii), (iii), dan (iv)

The given groups of numbers are (i) 3, 4, 5 and (iii) 7, 24, 25. A set of numbers is considered a Pythagorean triple if it satisfies the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In group (i), 3^2 + 4^2 = 5^2, so it satisfies the Pythagorean theorem. In group (iii), 7^2 + 24^2 = 25^2, so it also satisfies the Pythagorean theorem. Therefore, the Pythagorean triples in the given groups are (i) and (iii).

Explanation

The given groups of numbers are (i) 3, 4, 5 and (iii) 7, 24, 25. A set of numbers is considered a Pythagorean triple if it satisfies the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In group (i), 3^2 + 4^2 = 5^2, so it satisfies the Pythagorean theorem. In group (iii), 7^2 + 24^2 = 25^2, so it also satisfies the Pythagorean theorem. Therefore, the Pythagorean triples in the given groups are (i) and (iii).

10. Panjang sisi siku-siku suatu segitiga siku-siku berturut-turut adalah 4a cm dan 3a cm. Jika panjang sisi hipotenusanya adalah 70 cm, keliling segitiga tersebut adalah ...

A. 136 cm

B. 144 cm

C. 168 cm

D. 192 cm

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the lengths of the two sides are 4a cm and 3a cm. Using the Pythagorean theorem, we can set up the equation (4a)^2 + (3a)^2 = (70)^2. Simplifying this equation gives us 16a^2 + 9a^2 = 4900. Combining like terms gives us 25a^2 = 4900. Solving for a gives us a = 14. Substituting this value back into the equation for the lengths of the sides gives us 4a = 56 cm and 3a = 42 cm. The perimeter of the triangle is then 56 + 42 + 70 = 168 cm.

Explanation

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the lengths of the two sides are 4a cm and 3a cm. Using the Pythagorean theorem, we can set up the equation (4a)^2 + (3a)^2 = (70)^2. Simplifying this equation gives us 16a^2 + 9a^2 = 4900. Combining like terms gives us 25a^2 = 4900. Solving for a gives us a = 14. Substituting this value back into the equation for the lengths of the sides gives us 4a = 56 cm and 3a = 42 cm. The perimeter of the triangle is then 56 + 42 + 70 = 168 cm.

11. Perhatikan peta yang dibuat Euclid di bawah. Bangunan manakah yang berjarak 40 satuan?

A. Taman Kota dan Stadion

B. Pusat Kota dan Museum

C. Rumah Sakit dan Museum

D. Penampungan Hewan dan Kantor polisi

Based on the given map, the correct answer is D. Penampungan Hewan dan Kantor polisi. This is because the distance between Penampungan Hewan and Kantor polisi is 40 satuan, as indicated on the map.

Explanation

Based on the given map, the correct answer is D. Penampungan Hewan dan Kantor polisi. This is because the distance between Penampungan Hewan and Kantor polisi is 40 satuan, as indicated on the map.

12. Sebuah kapal berlayar ke arah utara sejauh 11 km kemudian kapal tersebut berbelok ke arah barat dan berlayar sejauh 9 km. Jarak kapal dari titik awal keberangkatan ke titik akhir adalah ....

A. akar 102 km

B. 102 km

C. akar 202 km

C. 202 km

The correct answer is C. akar 202 km. The ship initially sails 11 km north and then turns west and sails 9 km. To find the distance from the starting point to the ending point, we can use the Pythagorean theorem. The distance is equal to the square root of the sum of the squares of the two distances traveled. In this case, it is equal to the square root of (11^2 + 9^2) = square root of (121 + 81) = square root of 202. Therefore, the distance is akar 202 km.

Explanation

The correct answer is C. akar 202 km. The ship initially sails 11 km north and then turns west and sails 9 km. To find the distance from the starting point to the ending point, we can use the Pythagorean theorem. The distance is equal to the square root of the sum of the squares of the two distances traveled. In this case, it is equal to the square root of (11^2 + 9^2) = square root of (121 + 81) = square root of 202. Therefore, the distance is akar 202 km.

13. Diketahui segitiga KLM dengan panjang sisi-sisinya k, l, dan m. Pernyataan berikut yang benar dari segitiga KLM adalah ..

A. Jika m2 = l 2 + k2 , besar ∠K = 90 derajat

B. Jika m2 = l 2 − k2 , besar ∠M = 90 derajat

C. Jika m2 = k2 − l 2 , besar ∠L = 90 derajat

D. Jika k2 = l 2 + m2 , besar ∠K = 90 derajat

The correct answer is D. Jika k2 = l2 + m2, besar ∠K = 90 derajat. This statement is the correct one because it represents the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (in this case, k) is equal to the sum of the squares of the lengths of the other two sides (l and m). Therefore, if k2 = l2 + m2, it implies that angle K is a right angle (90 degrees).

Explanation

The correct answer is D. Jika k2 = l2 + m2, besar ∠K = 90 derajat. This statement is the correct one because it represents the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (in this case, k) is equal to the sum of the squares of the lengths of the other two sides (l and m). Therefore, if k2 = l2 + m2, it implies that angle K is a right angle (90 degrees).

14. Luas trapesium pada gambar di samping adalah ....

a. 246 inci2

b. 266,5 inci2

c. 276 inci2

d. 299 inci2

not-available-via-ai

Explanation

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15. (i) 3 cm, 5 cm, 6 cm (ii) 5 cm, 12 cm, 13 cm (iii) 16 cm, 24 cm, 32 cm (iv) 20 cm, 30 cm, 34 cm Ukuran sisi yang membentuk segitiga lancip ditunjukkan oleh ....

A. (i) dan (ii)

B. (i) dan (iii)

C. (ii) dan (iii)

D. (iv)

The sides that form an acute triangle are the ones that satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, only the sides in option (iv) satisfy this condition, as 20 + 30 > 34, 20 + 34 > 30, and 30 + 34 > 20. Therefore, the correct answer is D. (iv).

Explanation

The sides that form an acute triangle are the ones that satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, only the sides in option (iv) satisfy this condition, as 20 + 30 > 34, 20 + 34 > 30, and 30 + 34 > 20. Therefore, the correct answer is D. (iv).

Kuis Phytagoras Kelas 8