A triangle has side lengths of 10, 24, and 30. What type of triangle is it?
Acute
Equiangular
Equilateral
Obtuse

Solution:

Given, the length of the sides of a triangle are 10, 24 and 30.

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 = 10, b = 24 and c = 30

a² + b² =  (10)² + (24)² = 100 + 576 = 676

c² = (30)² = 900

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 side lengths of 10, 24, and 30. What type of triangle is it?

Summary:

A triangle with length of sides 10, 24 and 30 is obtuse.