Question

if three sides of a right triangle are 9, 40, and 41, which side is the hypotenuse?

Explanation:

Step1: Recall the Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side) and \(a\) and \(b\) are the legs.

Step2: Compare the values

We have three values: \(9\), \(40\), and \(41\).
Calculate \(9^{2}=81\), \(40^{2} = 1600\), and \(41^{2}=1681\).
Then \(9^{2}+40^{2}=81 + 1600=1681\).
Since \(9^{2}+40^{2}=41^{2}\), and the hypotenuse is the longest side in a right - triangle.

Answer:

\(41\)