Question

finding side lengths find the unknown side length. simplify answers that are radicals. tell whether the side lengths form a pythagorean triple.
11.
right triangle with legs 7 and x, hypotenuse 9

Explanation:

Step1: Apply Pythagorean theorem

$$7^2 + x^2 = 9^2$$

Step2: Calculate known squares

$$49 + x^2 = 81$$

Step3: Isolate $x^2$

$$x^2 = 81 - 49 = 32$$

Step4: Solve for $x$ (simplify radical)

$$x = \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}$$

Step5: Check Pythagorean triple

A Pythagorean triple requires all side lengths to be positive integers. $4\sqrt{2}$ is irrational, so the sides do not form a Pythagorean triple.

Answer:

The unknown side length is $4\sqrt{2}$. The side lengths do not form a Pythagorean triple.