Question

The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle.

1. 14 m, 5 m, 4 m

2. 3 in., 4 in., 5 in. Are these right triangles?

Answer 1

In a right triangle, the hypotenuse is always the longest side. Plus, the hypotenuse squared has to equal the sum of the squares of the other 2 sides. For the first "triangle" above: does
`14 ^(2) =5 ^(2) +4 ^(2)`? Let's check. 196 = 25 + 16 so does 196 = 41? Obviously not. So that is not a right triangle. Let's check the second one the same way. Does
`5 ^(2) =3 ^(2) +4 ^(2)`? 25 = 9 + 16. Does 25 = 25? Of course it does! So 1 is not a right triangle, but 2 is!