The length of the porch is 2 feet longer than twice the width, and the perimeter is 64 feet. Find the dimensions of the porch.

Question

Complete showing all necessary work. The variables must be identified, there must be a visual representation(ie diagram, table, etc), an equation must be used, the solution must be shown and the results must be labeled and explained.

Answer 1

(Assuming the porch is rectangular) Let's call the length L and the width W (all units in feet) and turn these sentences into equations. The first is saying

 

"the length of the porch is" --> L =

"2 ft longer than twice the width" --> 2 + 2W

 

L = 2 + 2W

 

Remember that the perimeter is the total length of the edge, which equals 2L + 2W for a rectangle. Thus, the second equation is

 

2L + 2W = 64

 

These two equations are enough to solve the problem. You can solve for either one first, but I will do it this way:

 

2L + (L - 2) = 64 --> 3L = 66 --> L = 22

 

22 = 2 + 2W --> 20 = 2W --> W = 10

 

First, note that the answers are positive, which is good (they don't necessarily have to be integers). To double-check, plug the answers back into the sentences.