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

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 .

2. Triangle ABC is acute, if .

3. Triangle ABC is acute, if .

The sum of square of two smaller sides is

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

It means,

Since , therefore, the triangle ABC is an acute triangle.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15