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?

Enter your answer in the box.

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.