Question

finding side lengths find the unknown side length. simplify answers that are radicals. tell whether the side lengths form a pythagorean triple. 7. a right triangle with one leg 65, another leg 72, and hypotenuse x (other parts are blacked out).

Explanation:

Step1: Apply Pythagorean theorem

$$x^2 = 65^2 + 72^2$$

Step2: Calculate squared terms

$$x^2 = 4225 + 5184$$

Step3: Sum the squared values

$$x^2 = 9409$$

Step4: Solve for x

$$x = \sqrt{9409} = 97$$

Step5: Check Pythagorean triple

All sides (65, 72, 97) are positive integers, so they form a Pythagorean triple.

Answer:

The unknown side length is 97, and the side lengths form a Pythagorean triple.