Write and solve and equation to determine the perimeter of the trianlge

Question

The perimeter of a triangle increased by 6 is the same as 42 decreased by 8 times the perimeter. Write and solve and equation to determine the perimeter of the triangle.

Answer 1

When we increase the perimeter by 6, we add 6 to the perimeter.  42 decreased by 8 times the perimeter means that we start from 42, but it becomes less.

 

 

Let P = original perimeter

 

 

P + 6 = 42 - 8P

 

 

Solve for P.

 

Add 8P on both sides of equation.

 

9P + 6 = 42

 

 

Subtract 6 on both sides of equation.

 

9P = 36

 

 

Divide both sides of equation by 9.

 

P = 4

 

 

The perimeter is 4.