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, \(a = 20\), \(b = 21\), and \(x\) is the hypotenuse. So \(x^{2}=20^{2}+21^{2}\).

Step2: Calculate the squares

\(20^{2}=20\times20 = 400\) and \(21^{2}=21\times21=441\). Then \(x^{2}=400 + 441\).

Step3: Add the results

\(x^{2}=841\).

Step4: Find the square - root

\(x=\sqrt{841}=29\).

Answer:

29