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

Acute

Equiangular

Equilateral

Obtuse

**Solution:**

Given, the length of the sides of a triangle are 5, 7 and 11.

To find the type of triangle we have to find the sum of the squares of the 2 shorter sides and compare it with the square of the largest side.

Let a = 5, b = 7 and c = 11

a^{2} + b^{2} = (5)^{2} + (7)^{2} = 25 + 49 = 74

c^{2} = (11)^{2} = 121

1) for a triangle to be acute,

a^{2 }+ b^{2 } > c^{2}

So, the triangle is not an acute triangle.

2) Equiangular means the measure of each of its interior angles must be 60°.

Therefore, the triangle cannot be equiangular

3) Since the sides are not equal, the triangle cannot be equilateral.

4) We observe, a^{2} + b^{2} < c^{2}

Therefore, the triangle is obtuse.

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

**Summary:**

A triangle with length of sides 5, 7 and 11 is obtuse.

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