Question

Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?

Answer 1

It has a side that is far smaller than the others which make it an acute triangle, also the angle is not a 90-degree angle

Answer 2

Triangle with side 2 in , 4 in and 5 in is an Obtuse angled triangle. It is not an Acute angles triangle.

Explanation:

Given:

Length of the sides of the triangle = 2 in , 5 in and 4 in

We know that if a , b and c is sides of the triangle such that c is the longest side then

1). if c² > a² + b² then the triangle is Acute angled.

2). if c² = a² + b² then the triangle is Right angled.

3). if c² < a² + b² then the triangle is Obtuse angled.

Here, a = 2 in , b = 4 in and c = 5 in

So, c² = 5² = 25

a² + b² = 2² + 4² = 4 + 16 = 20

Clearly c² > a² + b²

Therefore, Triangle with side 2 in , 4 in and 5 in is an Obtuse angled triangle. It is not an Acute angles triangle.