Question

Determine whether the given numbers represent the lengths of sides of a right triangle.9,40,41Do the given numbers represent the lengths of the sides of a right triangle?YesNo

Answer 1

To prove that these numbers form the sides of a right triangle we should do these steps

1. Square the longest side

2. Find the sum of the squares of the other 2 sides

3. If the sum equals the square of the longest side, then the numbers can form a right triangle

Since the longest side is 41, then

$(41)^2=1681$

Since the other 2 numbers are 40 and 9, then

$(40)^2+(9)^2=1600+81=1681$

From both steps, we can say

$(41)^2=(40)^2+(9)^2$

Then the answer is

YES, 9, 40, 41 can form the sides of a right triangle