Question

Give the angle classification of the triangle
with side lengths 3 cm, 5 cm, and 7 cm.

Answer 1

Given:

The sides of a triangle are 3 cm, 5 cm, 7 cm.

To find:

The angle classification of the given triangle.

Solution:

Let a,b,c are the three sides of a triangle ABC, where c is the longest side.

1. Triangle ABC is acute, if
`c^2<a^2+b^2`.

2. Triangle ABC is acute, if
`c^2=a^2+b^2`.

3. Triangle ABC is acute, if
`c^2>a^2+b^2`.

The sum of square of two smaller sides is

`3^2+5^2=9+25`

`3^2+5^2=34`

In the given triangle 7 cm is the longest sides. So,

`7^2=49`

It means,

`7^2>3^2+5^2`

Since
`c^2>a^2+b^2`, therefore, the triangle ABC is an acute triangle.