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 and \(a\) and \(b\) are the legs. Here, \(a = 12\), \(b = 16\), and we want to find the hypotenuse \(x\). So \(x^{2}=12^{2}+16^{2}\).

Step2: Calculate squares

\(12^{2}=144\) and \(16^{2}=256\). Then \(x^{2}=144 + 256\).

Step3: Add the values

\(144+256 = 400\), so \(x^{2}=400\).

Step4: Find the square - root

Taking the square - root of both sides, \(x=\sqrt{400}=20\) (we take the positive value since side length cannot be negative).

Answer:

20