# A triangle has sides with lengths of 35 miles, 84 miles, and 91 miles. Is it a right triangle?

Nov 28, 2016

Yes.

#### Explanation:

Using Pythagoras we have the condition:

If this is a right triangle then the longest side is the hypotenuse. Also the square of the hypotenuse is the sum of the square of the other 2 sides.

In which case the hypotenuse would be 91 and its square is 8281

The side which is 35 long has the squared value of ${35}^{2} = 1225$
The side which is 84 long has the squared value of ${84}^{2} = \underline{7056}$
The sum is:$\text{ } 8281$

This is the same value as the square of the longest side. So it is a right triangle