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

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Answer 1 · 2016-11-28T00:19:13

This is not a right angled triangle.

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

Check with Pythagoras:

$56^2+37^2 = 3136+1369 = 4505 != 4225 = 65^2$

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.