Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, \( a^2 + b^2 = c^2 \), where \( a = 16 \), \( b = 30 \), \( c = x \). So \( x^2 = 16^2 + 30^2 \).

Step2: Calculate squares

\( 16^2 = 256 \), \( 30^2 = 900 \). Then \( x^2 = 256 + 900 = 1156 \).

Step3: Take square root

\( x = \sqrt{1156} = 34 \).

Step4: Check Pythagorean triple

A Pythagorean triple consists of three positive integers. 16, 30, 34 are integers and satisfy \( 16^2 + 30^2 = 34^2 \), so yes.

Answer:

The exact value of \( x \) is \( 34 \). The side lengths form a Pythagorean triple (Yes).