Question

x 12 in 13 in

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 13\) in, \(a = 12\) in, and \(b=x\). So, \(x^{2}+12^{2}=13^{2}\).

Step2: Rearrange the equation to solve for \(x\)

We get \(x^{2}=13^{2}-12^{2}\). Calculate \(13^{2}=169\) and \(12^{2}=144\). Then \(x^{2}=169 - 144=25\).

Step3: Take the square root of both sides

Since \(x\) represents a length, we take the positive square root. So \(x=\sqrt{25}=5\) in.

Answer:

5 in