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A shed that measures $8$ feet by $11$ feet has a brick pathway of constant width built around it, so that the outer edge of the pathway is also a rectangle. The total area of the pathway is $120$ square feet. What is its width (in feet)?

 Aug 22, 2022
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Let x equal the width of the walkway. 

 

The area of the whole thing is            (2x + 8)(2x + 11)       Why 2x?  There's an x at each end of the

                                                                                            shed.  Draw the picture and you'll see. 

 

Multiply it out                                       4x2 + 38x + 88         (# 1)  

 

The area of the shed alone is             (8)(11)  =  88           (# 2) 

 

Subtract #2 from #1                            4x2 + 38x                  This is the area of the walkway. 

 

The problem says that the  

area of the walkway is 120 so             4x2 + 38x  =  120 

 

Subtract 120 from both sides              4x2 + 38x – 120  =  0 

 

Divide both sides by 2.  This is

just to make it easier to factor.             2x2 + 19x – 60  =  0 

 

Factor that                                           (2x – 5)(x +12)  =  0 

 

So                                                         x = +5/2  and  x = –12 

 

A walkway can't have negative

width, so the walkway is                        2.5 feet wide   

.

 Aug 22, 2022

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