Final answer:
Using the Pythagorean theorem, we can determine which set of measurements represents the side lengths of a right triangle. Options a (6cm, 8cm, 10cm) and d (10cm, 24cm, 26cm) are the correct answers.
Step-by-step explanation:
The question is asking which set of measurements represents the side lengths of a right triangle
. To determine this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. So, we can calculate the square of the length of each side and see if it satisfies this condition.
Let's calculate for each option:
- a. 6cm, 8cm, 10cm: 6^2 + 8^2 = 36 + 64 = 100. The square root of 100 is 10, which matches the given hypotenuse length. This set of measurements represents a right triangle.
- b. 12cm, 35cm, 37cm: 12^2 + 35^2 = 144 + 1225 = 1369. The square root of 1369 is approximately 36.98, which does not match the given hypotenuse length. This set of measurements does not represent a right triangle.
- c. 4cm, 6cm, 10cm: 4^2 + 6^2 = 16 + 36 = 52. The square root of 52 is approximately 7.21, which does not match the given hypotenuse length. This set of measurements does not represent a right triangle.
- d. 10cm, 24cm, 26cm: 10^2 + 24^2 = 100 + 576 = 676. The square root of 676 is 26, which matches the given hypotenuse length. This set of measurements represents a right triangle.
Based on these calculations, options a and d represent right triangles.