Pilihan Ganda 1

Based on the given information, we can determine that triangle PQR is a right triangle because PQ is perpendicular to RS. We are also given that QR = 2.5 cm and RS = 2 cm. To find the area of the triangle, we can use the formula for the area of a right triangle, which is (base * height) / 2. In this case, the base is QR and the height is RS. Plugging in the values, we get (2.5 cm * 2 cm) / 2 = 5 cm^2 / 2 = 2.5 cm^2. Therefore, the correct answer is 3.00 cm^2.

Based on the given information, the length of BC in the triangle is determined to be 9 cm.

The pair (1, 3) is a Pythagorean triple because if we square the first number (1^2 = 1), square the second number (3^2 = 9), and add them together (1 + 9 = 10), we get the square of the third number (10). Therefore, (1, 3) satisfies the Pythagorean theorem and is a Pythagorean triple.

The correct answer is 1 and 4. The first and fourth triangles (3 cm, 4 cm, 5 cm and 7 cm, 24 cm, 25 cm) are both right-angled triangles, which means they have one angle measuring 90 degrees. The second and third triangles are not right-angled triangles.

The correct answer is 90 cm because a trapezium is a quadrilateral with only one pair of parallel sides. In this case, sides AB and CD are parallel. To find the perimeter or the total distance around the trapezium, we add the lengths of all four sides. Given that AB = 40 cm, BC = 20 cm, CD = 10 cm, and DA = 20 cm, the sum of all four sides is 40 + 20 + 10 + 20 = 90 cm. Therefore, the perimeter of trapezium ABCD is 90 cm.

The triangle PQR is an equilateral triangle, which means all sides are equal. Given that the length of each side is 12 cm, the length of RS can be found using the Pythagorean theorem. Since RS is the hypotenuse of a right triangle with two sides of length 6 cm (half the length of one side of the equilateral triangle), we can calculate the length of RS as 6 times the square root of 3, which is approximately 6√3 cm.

The length of side BC can be determined by observing the right triangle formed by sides BC, AB, and AC. According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (side AC) is equal to the sum of the squares of the other two sides (sides AB and BC). In this case, if side AB has a length of 5 cm and side AC has a length of 13 cm, we can calculate the length of side BC by subtracting the square of side AB from the square of side AC, and then taking the square root of the result. This calculation yields a length of 12 cm for side BC.

The formula to find the area of a rhombus is (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals. Given that the area is 240 cm2 and one diagonal is 16 cm, we can substitute the values into the formula to find the length of the other diagonal. (16 * d2) / 2 = 240. Solving for d2, we get d2 = 30 cm. The perimeter of a rhombus is 4 times the length of one side. Since the diagonals of a rhombus bisect each other at right angles, we can use the Pythagorean theorem to find the length of one side. Using a^2 + b^2 = c^2, where a = 8 cm (half of one diagonal) and b = 15 cm (half of the other diagonal), we can solve for c (the length of one side). c^2 = 8^2 + 15^2 = 64 + 225 = 289. Taking the square root of both sides, we get c = 17 cm. Therefore, the perimeter is 4 * 17 = 68 cm.

The given lengths of the sticks are 4 cm, 5 cm, 9 cm, and 10 cm. In order to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. By checking all possible combinations, it can be determined that the sticks with lengths 4 cm, 5 cm, and 9 cm can form a triangle, while the stick with length 10 cm cannot form a triangle with the other sticks. Therefore, the possible triangles that Army can form are one acute triangle and three obtuse triangles.

The formula to calculate the area of a rectangle is length multiplied by width. In this case, the length is given as 24 cm. We can find the width using the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the two sides. So, we have 30^2 = 24^2 + width^2. Solving this equation, we find the width to be 18 cm. Therefore, the area of the rectangle is 24 cm * 18 cm = 432 cm^2.