Question

for the following right triangle, find the side length x.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, if the legs are 7 and 24, and the hypotenuse is \(x\), then \(x=\sqrt{7^{2}+24^{2}}\).

Step2: Calculate squares

\(7^{2}=49\) and \(24^{2}=576\). So \(7^{2}+24^{2}=49 + 576=625\).

Step3: Find square - root

\(x=\sqrt{625}=25\).

Answer:

25