Question

find the exact value of x. x = do the side lengths form a pythagorean triple? yes no

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is hypotenuse, \(a,b\) are legs. Here, \(a = 9\), \(b = 40\), \(c = x\). So \(x^2=9^2 + 40^2\).

Step2: Calculate squares

\(9^2 = 81\), \(40^2 = 1600\). Then \(x^2=81 + 1600 = 1681\).

Step3: Find square root

\(x=\sqrt{1681}=41\) (since length is positive).

Step4: Check Pythagorean triple

A Pythagorean triple has integer sides. 9, 40, 41 are integers, so yes.

Answer:

\(x = 41\)
Do the side lengths form a Pythagorean triple? Yes