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

##### 1 Answer

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

The side which is 84 long has the squared value of

The sum is:

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