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