Question

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

Explanation:

Step1: Identify triangle type

It's a right - triangle with hypotenuse \( c = 17 \) and one leg \( a = 8 \), find the other leg \( x \). Use Pythagorean theorem \( a^{2}+x^{2}=c^{2} \).

Step2: Apply Pythagorean theorem

Substitute \( a = 8 \), \( c = 17 \) into the formula: \( 8^{2}+x^{2}=17^{2} \). Calculate \( 8^{2}=64 \), \( 17^{2}=289 \). Then \( x^{2}=289 - 64=225 \). Take square root: \( x=\sqrt{225}=15 \).

Step3: Check Pythagorean triple

A Pythagorean triple is a set of three positive integers \( a,b,c \) such that \( a^{2}+b^{2}=c^{2} \). Here \( 8,15,17 \): \( 8^{2}+15^{2}=64 + 225 = 289=17^{2} \), so they form a triple.

Answer:

For \( x \): \( 15 \); For the Pythagorean triple question: Yes