Question

A triangle has side lengths of 80 cm 39 cm 89 cm is the triangle acute, obtuse, or right?

Answer 1

This triangle is right.

80² + 39² = 89²
6400 + 1521 = 7921
7921 = 7921

Answer 2

We can classify the triangle to be right ,acute or obtuse with respect to their sides . c is the longest sides .For any triangle with sides a,b,c if

1)
`a^(2) +b^(2) =c^(2)` the triangle is a right triangle .

2)
`a^(2) +b^(2) <c ^(2)` the triangle is obtuse.

3)
`a^(2) +b ^(2) >c ^(2)`

Given triangle has side lengths of 80 cm ,39 cm,89 cm . 89 cm is the largest side or c= 89 cm.

`80^(2) +39^(2) =89^(2)`

6400+1521 = 7921

7921=7921

`a^(2) +b^(2) =c^(2)`

The given triangle is a right triangle.