Question

The measure of the perimeter of a triangle is30x + 40. It is known that two of the sides of thetriangle have measures of 12x + 6 and 10x + 20.Find the length of the third side.

Answer 1

The perimeter of a triangle is equal to the sum of all the sides of the triangle.

A triangle has 3 sides so:

Perimeter = side 1 + side 2+ side 3

We have the values of the perimeter and two sides:

perimeter = 30x + 40

Side 1= 12x + 6

Side 2= 10x + 20

S3= ?

So, replacing with the values given:

30x+40= (12x+6)+(10x+20)+ S3

Solving for S3 ( side 3)

30x+40= 12x+6+10x+20+S3

30x+40=12x+10x+6+20+S3

30x+40= 22x+26+S3

30x+40-22x-26=S3

30x-22x+40-26=S3

8x+14 =S3

Lenght of the third side = 8x+14