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

 Mar 12, 2019
 #1
avatar+4299 
+2

Hint: Try to start off with a diagram. 

 Mar 12, 2019
 #2
avatar+102434 
+1

The area f the shed =  8 * 11 = 88 ft^2

The area of the path is 120ft^2

So...the combined area is  208 ft^2

 

Let the width of the path = x

 

And we have this equation

 

(shed width + 2*path width) (shed length + 2*path width) = 208

 

(8 + 2x) ( 11 + 2x) =  208       simplify

 

88 + 22x + 16x + 4x^2 = 208

 

4x^2 + 38x - 120  =  0     factor

 

(2x - 5) (2x + 24)  = 0

 

Only the first factor will give a positive answer

 

2x - 5 = 0

2x = 5

x = 5/2  =  2.5 ft = path width

 

 

cool cool cool

 Mar 12, 2019
 #3
avatar+4299 
+3

Bulls-eye ! smiley

tertre  Mar 12, 2019

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