Application of System of Equations

Question

The perimeter of a rectangle is 52 m. If the width were doubled and the length were increased by 5 m, the perimeter would be 82 m. What are the length and width of the rectangle?

Answer 1

2L + 2W = 52

82 = 2(2W) + 2(L+5) = 4W + 2L + 5 => 4W + 2L = 77

 

Isolate a variable in equation 1.

 

2L = 52-2W

L = 26 - W

 

Plug into eq 2.

 

4W + 2 (26-W) = 77

4W + 52 - 2W = 77

2W = 25

W = 12.5

 

L = 26-12.5 = 13.5

 

Double check the work.

 

2(12.5) + 2(13.5) = 52

25 + 27 = 52

52 = 52