Question

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

Answer 1

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=ul(7056)`
The sum is:`" "8281`

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