# A triangle has sides with lengths of 56 yards, 65 yards, and 37 yards. Is it a right triangle?

Nov 28, 2016

This is not a right angled triangle.

#### Explanation:

If it is a right angled triangle, then the longest, $65$ yard long, side is the hypotenuse.

Check with Pythagoras:

${56}^{2} + {37}^{2} = 3136 + 1369 = 4505 \ne 4225 = {65}^{2}$

So this cannot be a right angled triangle.

In fact we find:

${65}^{2} - {56}^{2} = 4225 - 3136 = 1089 = {33}^{2}$

So a triangle with sides $56$ yards, $65$ yards and $33$ yards would be a right angled triangle.