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. Here, \(a = 40\), \(b=9\), and \(c=x\).
So, \(x^{2}=40^{2}+9^{2}\).

Step2: Calculate squares

\(40^{2}=1600\) and \(9^{2}=81\). Then \(x^{2}=1600 + 81\).

Step3: Sum the values

\(x^{2}=1681\).

Step4: Find the square root

\(x=\sqrt{1681}\). Since \(41\times41 = 1681\), \(x = 41\).

Answer:

\(41\)