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. Here, \(a = 5\), \(b = 12\), and \(x\) is the hypotenuse. So \(x^{2}=5^{2}+12^{2}\).

Step2: Calculate the squares

\(5^{2}=25\) and \(12^{2}=144\), then \(x^{2}=25 + 144\).

Step3: Add the values

\(x^{2}=169\).

Step4: Find the square - root

\(x=\sqrt{169}\), and since \(x>0\) (as it represents a side - length), \(x = 13\).

Answer:

13