California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

If a right triangle has legs measuring 6 cm and 8 cm, what is the length of the hypotenuse?

1. 10 cm

2. 12 cm

3. 14 cm

4. 15 cm

The correct answer is: 10 cm

To determine the length of the hypotenuse in a right triangle when the lengths of the legs are known, we can utilize the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, it can be expressed as: c² = a² + b². In this case, the lengths of the legs are 6 cm and 8 cm. By applying the theorem: 1. Calculate the squares of the legs: - 6 cm squared is 36 (6² = 36). - 8 cm squared is 64 (8² = 64). 2. Add the squares of the legs together: - 36 + 64 equals 100. 3. To find the hypotenuse, take the square root of the sum: - The square root of 100 is 10 cm (√100 = 10). Thus, the length of the hypotenuse in this right triangle is correctly calculated to be 10 cm. This demonstrates a solid application of the Pythagorean theorem,