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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)?

 Jul 23, 2019
 #1
avatar+102399 
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The pathway will consist of 4 squares each with a side of x, two rectangles with dimensions of 8 *x   and two rectangles with dimensions of 11*x ......  where x is the width of the path

 

4x^2  + 2(8*x)  + 2(11*x)  = 120

 

4x^2 + 16x + 22x  = 120

 

4x^2 + 38x  = 120

 

4x^2 + 38x - 120  = 0   factor

 

(x + 12)(4x - 10)= 0      set each factor to 0 ans solve for x

 

x + 12  = 0                 4x  - 10  = 0

x = -12  (reject)          4x  = 10

                                    x  = 10/4  = 5/2  =  2.5 ft

 

So.....the path width is 2.5 ft

 

 

cool cool cool

 Jul 23, 2019

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