Question

A triangle has side lengths of 23 in, 6 in, and 28 in. Classify it as acute, obtuse, or right.

Answer 1

The triangle has side lengths of 23 in, 6 in, and 28 in. is an obtuse triangle.

Explanation:

Given : A triangle has side lengths of 23 in, 6 in, and 28 in.

To Classify: It as acute, obtuse, or right.

Solution:

Let 'c' be the longest side on the set of three numbers.

If
`c^2 = a^2+b^2`, the triangle is right

If
`c^2 > a^2+b^2`, the triangle is obtuse

If
`c^2 < a^2+b^2`, the triangle is acute.

So, let a=6 , b=23 and c=28

Now we put the value in
`c^2 = a^2+b^2` to check it is equal,greater or less.

LHS -
`c^2`

`(28)^2=784`

RHS -
`a^2+b^2`

`(6)^2+(23)^2`

`=36+529=565`

which means
`784 > 565`

i.e, LHS > RHS

So, the triangle is an obtuse.

Therefore, The triangle has side lengths of 23 in, 6 in, and 28 in. is an obtuse triangle.