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Question

A 6 foot by 8 foot rectangular garden is surrounded by a path of equal width on all four sides. If the total area of the path and garden is 120 square feet, find the width of the path.

Answer 1

let x = the width of the path

 

because the path goes all the way around the garden, add x twice to the 6 feet (on the left and right side of

 

the garden) and twice to the 8 feet (on the top and bottom of the garden) and then calculate the area by multiplying

 

(2x + 6)(2x + 8) = 120

 

4x² + 16x + 12x + 48 = 120

 

4x² + 28x -72 = 0    divide by 4

 

x² + 7x - 18 = 0

 

(x + 9)(x - 2) = 0

 

x can't be -9

 

x = 2

 

the path is 2 feet wide

 

to check:

 

the width of the garden is 6 + 2 + 2 = 10

 

the length of the garden = 8 + 2 + 2 = 12

 

and 10 x 12 = 120