Question

A garden measures 6 feet by 7 feet. A gravel path of constant width is placed around the garden so that the total area is 72 square feet.
What is the width of the gravel path?

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Answer 1

Let 
x---------> the width of the gravel path

we know that
72=(2x+6)*(2x+7)----> 72=4x²+14x+12x+42-------> 4x²+26x-30=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solution is
x=1

the answer is
the width of the gravel path is 1 ft

Answer 2

To solve this problem you must apply the proccedure shown below:

 1. You have that:

 - The garden measures 6 feet by 7 feet.
 - The gravel path has a constant width and it is placed around the garden.
 - The total area is 72 square feet. 

 2. Therefore, let's call:

 x: the widht of the gravel path
 L1:The lenght of the garden (L1=7 ft).
 W1: The widht of the garden (W1=6 ft).
 L2=The lenght of the garden + The widht of the gravel path on both sides (L2=L1+2x=7+2X).
 W2=The widht of the garden + The widht of the gravel path on both sides (W2=W1+2X=6+2x).
 A: The total area (A=72 ft^2).

 2. The formula for calculate the area of a rectangle is:

 A=LenghxWidth

 A=L2xW2
 72=(7+2x)(6+2x)
 4x^2+26x-30=0

 x=1 ft

 The answer is: 1 ft.