Question

find x. x = centimeters

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, \(c = 13\) cm, \(a=12\) cm, and \(b = x\). So, \(x^{2}+12^{2}=13^{2}\).

Step2: Rearrange the equation

\(x^{2}=13^{2}-12^{2}\).

Step3: Calculate the squares

\(13^{2}=169\) and \(12^{2}=144\), so \(x^{2}=169 - 144\).

Step4: Subtract

\(x^{2}=25\).

Step5: Take the square root

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

Answer:

5