SOLUTION: Lorraine has a rectangular flower garden which is five feet longer than it is wide. The longer side of the flower garden is along a fence, as shown in the picture. The flower garde
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Question 307054: Lorraine has a rectangular flower garden which is five feet longer than it is wide. The longer side of the flower garden is along a fence, as shown in the picture. The flower garden is surrounded on three sides by a gravel walkway, which is 2 feet wide. If the area of the gravel walkway is 72 square feet, then what is the area of the garden?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Lorraine has a rectangular flower garden which is five feet longer than it is wide.
The longer side of the flower garden is along a fence, as shown in the picture.
The flower garden is surrounded on three sides by a gravel walkway, which is 2 feet wide.
If the area of the gravel walkway is 72 square feet, then what is the area of the garden?
:
Let x = the width of the garden
then
(x+5) = the length of the garden
:
From the drawing you can see the overall dimensions: which include the walkway will be:
Overall Length: (x+5)+4 = (x+9)
Overall width: (x + 2)
:
Overall area - garden area = walkway area (72')
(x+9)(x+2) - x(x+5) = 72
FOIL
x^2 + 2x + 9x + 18 - x^2 - 5x = 72
Combine like terms
x^2 - x^2 + 2x + 9x - 5x + 18 = 72
:
6x + 18 = 72
:
6x = 72 - 18
:
6x = 54
x =
x = 9 ft
:
Garden area
(9+5) * 9 = 126 sq/ft
;
:
Check solution:
(9+9)*(9+2)= 198 overall area
9 *(9 + 5) = 126 garden area
-------------------------------
difference = 72 walkway area
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