Question

for the following right triangle, find the side length x.

Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle with legs \(a = 9\), \(b = 40\) and hypotenuse \(x\), the Pythagorean theorem is \(a^{2}+b^{2}=x^{2}\).
So, \(x^{2}=9^{2}+40^{2}\).

Step2: Calculate \(9^{2}\) and \(40^{2}\)

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

Step3: Sum the values

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

Step4: Take the square root

Since \(x>0\) (length of a side), \(x=\sqrt{1681}\).

Step5: Find the square root value

\(\sqrt{1681}=41\).

Answer:

\(41\)