help me solvea area problem

Question

cynthia besch wants to buy a rug for a room that is 28ft wide and 29 ft long. she wants to leave a uniform strip of floor around the rug she can afford to buy 702 square feet of carpeting. what dimensions should the rug have

Answer 1

Let x = width of strip

 

Then the dimensions of the rug are 28 - 2x by

29 - 2x

 

So, (28 - 2x)(29 - 2x) = 702

 

4x² - 114x + 812 = 702

 

4x² - 114x + 110 = 0

 

Divide both sides by 2:  2x² - 57x + 55 = 0

 

                                      (2x - 55)(x - 1) = 0

 

                                       x = 1 or x = 27.5

 

If x = 27.5, then the width of the rug is

28 - 2(27.5) < 0.  So, x = 27.5 is not feasible.  

 

Therefore, x = 1 ft

 

Width = 28 - 2x = 26 ft

Length = 29 - 2x = 27 ft