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

a² + b² =  (5)² + (7)² = 25 + 49 = 74

c² = (11)² = 121

1) for a triangle to be acute,

a² + b²  > c²

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, a² + b² < c²

Therefore, the triangle is obtuse.

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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.