Question

12 in 13 in x 10. * 5in

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Rearrange to solve for \(x\)

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

Step3: Find the value of \(x\)

Take the square root of both sides. Since \(x\) represents a length, we take the positive square - root. So \(x=\sqrt{25}=5\).

Answer:

5 in