Question

A triangle has the side lengths 5, 7, and 11. Which term best describes the triangle?

Answer 1

It's an obtuse triangle

Answer 2

Obtuse Triangle.

Explanation:

The Pythagorean Theorem helps us to Classify Triangles according to its sides.

If
`a^(2)+b^(2)>c^(2)`, then lengths a, b, and c make up an acute triangle.

If
`a^(2)+b^(2) <c^(2)` then lengths a, b, and c make up the sides of an obtuse triangle.

If
`a^(2)+b^(2)=c^(2)` Then the length a,b,c make a right triangle.

The given sides are 5,7 and 11.

`5^(2)+7^(2)<11^(2)`

Or 74<121

Or
`a^(2)+b^(2) <c^(2)`

So given triangle is obtuse triangle.