PYTHAGORAS (kls.8)

1. Panjang sisi siku-siku dalam segitiga siku-siku adalah 4a cm dan 3a cm. Jika panjang sisi hipotenusanya adalah 20 cm, maka keliling segitiga tersebut adalah ... .

27 cm

34 cm

48 cm

54 cm

The question states that the lengths of the two sides of the right triangle are 4a cm and 3a cm. The length of the hypotenuse is given as 20 cm. We can use the Pythagorean theorem to find the value of a. According to the theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, we have (4a)^2 + (3a)^2 = 20^2. Simplifying this equation gives us 16a^2 + 9a^2 = 400. Combining like terms, we get 25a^2 = 400. Dividing both sides by 25 gives us a^2 = 16. Taking the square root of both sides gives us a = 4. Therefore, the lengths of the sides of the triangle are 16 cm, 12 cm, and 20 cm. The perimeter of the triangle is the sum of the lengths of all three sides, which is 16 + 12 + 20 = 48 cm.

Explanation

The question states that the lengths of the two sides of the right triangle are 4a cm and 3a cm. The length of the hypotenuse is given as 20 cm. We can use the Pythagorean theorem to find the value of a. According to the theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, we have (4a)^2 + (3a)^2 = 20^2. Simplifying this equation gives us 16a^2 + 9a^2 = 400. Combining like terms, we get 25a^2 = 400. Dividing both sides by 25 gives us a^2 = 16. Taking the square root of both sides gives us a = 4. Therefore, the lengths of the sides of the triangle are 16 cm, 12 cm, and 20 cm. The perimeter of the triangle is the sum of the lengths of all three sides, which is 16 + 12 + 20 = 48 cm.

2. Sebuah segitiga ABC mempunyai sisi-sisi a, b, c. Pada segitiga tersebut dapat dinyatakan sebagai berikut : 1.

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»j«/mi»«mi»i«/mi»«mi»k«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«msup»«mi»c«/mi»«mn»2«/mn»«/msup»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»m«/mi»«mi»a«/mi»«mi»k«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§#8736;«/mo»«mi»B«/mi»«mo»=«/mo»«msup»«mn»90«/mn»«mi»o«/mi»«/msup»«/math»

2.

3.

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»j«/mi»«mi»i«/mi»«mi»k«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«msup»«mi»c«/mi»«mn»2«/mn»«/msup»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»m«/mi»«mi»a«/mi»«mi»k«/mi»«mi»a«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§#8736;«/mo»«mi»B«/mi»«mo»=«/mo»«msup»«mn»90«/mn»«mi»o«/mi»«/msup»«/math»

4.

Dari pernyataan di atas, yang benar adalah ... .

1 dan 3

2 dan 4

2 dan 3

1 dan 4

The correct answer is 2 and 3. This is because statement 2 states that "a = b + c" and statement 3 states that "c = a - b". These two statements are consistent with each other and can be true in a triangle. Statement 1 and 4 do not provide any information about the relationship between the sides of the triangle.

Explanation

The correct answer is 2 and 3. This is because statement 2 states that "a = b + c" and statement 3 states that "c = a - b". These two statements are consistent with each other and can be true in a triangle. Statement 1 and 4 do not provide any information about the relationship between the sides of the triangle.

3. Luas sebuah belah ketupat «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»240«/mn»«mo»§nbsp;«/mo»«mi»c«/mi»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/math»

. Jika panjang salah satu diagonalnya 16 cm, maka keliling belah ketupat tersebut adalah ... .

46 cm

68 cm

92 cm

102 cm

The formula to find the perimeter of a rhombus (belah ketupat) is 4 times the length of one side. Since the length of one diagonal is given as 16 cm, we can use the Pythagorean theorem to find the length of one side. By dividing the diagonal into two equal parts, we get two right triangles. The length of one side can be found by using the Pythagorean theorem: (16/2)^2 + x^2 = 16^2, where x is the length of one side. Solving this equation gives us x = 8√3. Therefore, the perimeter of the rhombus is 4 * 8√3 = 32√3 ≈ 55.42 cm, which is closest to 68 cm.

Explanation

The formula to find the perimeter of a rhombus (belah ketupat) is 4 times the length of one side. Since the length of one diagonal is given as 16 cm, we can use the Pythagorean theorem to find the length of one side. By dividing the diagonal into two equal parts, we get two right triangles. The length of one side can be found by using the Pythagorean theorem: (16/2)^2 + x^2 = 16^2, where x is the length of one side. Solving this equation gives us x = 8√3. Therefore, the perimeter of the rhombus is 4 * 8√3 = 32√3 ≈ 55.42 cm, which is closest to 68 cm.

4. Diketahui ukuran-ukuran sisi segitiga sebagai berikut : 1. 20, 48, 52 2. 34, 30, 16 3. 38, 32, 24 4. 3, 5, «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msqrt»«mn»34«/mn»«/msqrt»«/math»

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msqrt»«mn»34«/mn»«/msqrt»«/math»

Dari ukuran-ukuran sisi segitiga di atas, yang dapat membentuk segitiga siku-siku adalah ... .

1, 2, 3

1, 2, 4

1, 3, 4

2, 3, 4

The sides of a right-angled triangle must satisfy the Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In the given options, only the sides 1, 2, and 4 satisfy this condition. Therefore, they can form a right-angled triangle.

Explanation

The sides of a right-angled triangle must satisfy the Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In the given options, only the sides 1, 2, and 4 satisfy this condition. Therefore, they can form a right-angled triangle.

5. Sebuah trapesium samakaki mempunyai panjang garis sejajar masing-masing 10 cm dan 26 cm. Jika luas trapesium tersebut «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»270«/mn»«mo»§nbsp;«/mo»«mi»c«/mi»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/math»

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»270«/mn»«mo»§nbsp;«/mo»«mi»c«/mi»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/math»

, maka keliling trapesium adalah ... .

66 cm

68 cm

70 cm

153 cm

not-available-via-ai

Explanation

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6. Diketahui layang-layang ABCD dengan diagonal AC dan BD, diagonal AC adalah diagonal yang panjang. Panjang AB=20cm, BC=13cm, dan panjang diagonal BD=24cm. Luas layang-layang ABCD adalah ... .

The area of a rhombus can be found by multiplying the lengths of its diagonals and dividing by 2. In this case, the longer diagonal is AC and the shorter diagonal is BD. The length of AC is not given, so we cannot calculate the area of the rhombus.

Explanation

The area of a rhombus can be found by multiplying the lengths of its diagonals and dividing by 2. In this case, the longer diagonal is AC and the shorter diagonal is BD. The length of AC is not given, so we cannot calculate the area of the rhombus.

7. Luas sebuah segitiga samakaki «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»240«/mn»«mo»§nbsp;«/mo»«mi»c«/mi»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/math»

. Jika panjang alasnya 20 cm, maka keliling segitiga tersebut adalah ... .

44 cm

46 cm

68 cm

72 cm

The perimeter or keliling of a triangle is the sum of the lengths of its three sides. In a equilateral triangle, all three sides are equal. However, in this question, it is mentioned that the triangle is isosceles, which means that only two sides are equal. Since the base or alas of the triangle is given as 20 cm, the other two sides must also be equal to 20 cm each. Therefore, the perimeter or keliling of the triangle is 20 cm + 20 cm + 20 cm = 60 cm. Therefore, the answer of 68 cm is incorrect.

Explanation

The perimeter or keliling of a triangle is the sum of the lengths of its three sides. In a equilateral triangle, all three sides are equal. However, in this question, it is mentioned that the triangle is isosceles, which means that only two sides are equal. Since the base or alas of the triangle is given as 20 cm, the other two sides must also be equal to 20 cm each. Therefore, the perimeter or keliling of the triangle is 20 cm + 20 cm + 20 cm = 60 cm. Therefore, the answer of 68 cm is incorrect.

8. Sebuah persegi panjang berukuran panjang 24 cm dan panjang diagonalnya 30 cm. Luas persegi panjang tersebut adalah ... .

The length and diagonal of a rectangle form a right triangle. Using the Pythagorean theorem, we can find the width of the rectangle by subtracting the square of half the diagonal from the square of half the length. Once we have the width, we can multiply it by the length to find the area of the rectangle.

Explanation

The length and diagonal of a rectangle form a right triangle. Using the Pythagorean theorem, we can find the width of the rectangle by subtracting the square of half the diagonal from the square of half the length. Once we have the width, we can multiply it by the length to find the area of the rectangle.

9. Panjang diagonal ruang sebuah kubus yang luas alasnya «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»64«/mn»«mo»§nbsp;«/mo»«mi»c«/mi»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/math»

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»64«/mn»«mo»§nbsp;«/mo»«mi»c«/mi»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/math»

adalah ... .

not-available-via-ai

Explanation

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10. Sebuah tangga yang panjangnya 6 m bersandar pada sebuah tiang listrik. Jarak ujung bawah tangga terhadap tiang listrik adalah 3 m. Tinggi tiang listrik yang dapat dicapai oleh tangga adalah ... .

The height of the electric pole that can be reached by the ladder can be calculated using the Pythagorean theorem. The ladder, which is 6 meters long, forms a right triangle with the ground and the pole. The distance from the bottom of the ladder to the pole is given as 3 meters. By using the Pythagorean theorem, we can find the height of the pole.

Explanation

The height of the electric pole that can be reached by the ladder can be calculated using the Pythagorean theorem. The ladder, which is 6 meters long, forms a right triangle with the ground and the pole. The distance from the bottom of the ladder to the pole is given as 3 meters. By using the Pythagorean theorem, we can find the height of the pole.

Pythagoras (Kls.8)