SOLUTION: A garden in the form of a square is surrounded by a path which is 1m wide on two opposite sides and 0.5m wide on the other two opposite sides. If the area of the path is 17m^2, cal

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Question 991416: A garden in the form of a square is surrounded by a path which is 1m wide on two opposite sides and 0.5m wide on the other two opposite sides. If the area of the path is 17m^2, calculate the
(a) perimeter of the path
(b) area of the space covered by the garden and the path
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A garden in the form of a square is surrounded by a path which is 1m wide on two opposite sides and 0.5m wide on the other two opposite sides. If the area of the path is 17m^2,
:
Let x = the length of the side of the square garden
then
x^2 = the area of the garden
The path will add 2 meters to one side and 1 meter to the other side
Write an equation for the overall area to find x
(x+2)(x+1) = x^2 + 17
FOIL the left side
x^2 + 3x + 2 = x^2 + 17
Subtract x^2 and 2 from each side
3x = 17 - 2
3x = 15
x = 5 meters is the side of the garden
:
calculate the:
(a) perimeter of the path
p = 2(5+2) + 2(5+1)
p = 14 + 12
p = 26 meters
:
(b) area of the space covered by the garden and the path
A = (5+2)*(5+1)
A = 7 * 6
A = 42 sq/m the area