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 \(a = 7\), \(b = 24\), and \(c=x\).
So, \(x^{2}=7^{2}+24^{2}\).

Step2: Calculate squares

\(7^{2}=49\) and \(24^{2}=576\).
Then \(x^{2}=49 + 576\).

Step3: Sum the values

\(49+576=625\). So \(x^{2}=625\).

Step4: Take square root

\(x=\sqrt{625}\).
Since \(x>0\) (side length), \(x = 25\).

Answer:

\(25\)