<PRE><B>Question 1011141</B>
A garden in form of a square is surrounded by a path which is 1m wide on two opposite sides and 1/2m wide on the other two opposite sides.
if the area of the path is 17m^2.Calculate the perimeter of the garden and the area of the space covered by the garden and the paths
:
let s = one side of the square garden
then, because of the path configuration, the rectangle including the garden and the path dimensions will be: (s+2) by (s+1)
:
Over all area - garden area = path area
(s+2)*(S+1) - s^2 = 17
FOIl
(s^2 + 3s + 2) - s^2 = 17
combine like terms
s^2 - s^2 + 3s = 17 - 2
3s = 15
s = 5 meters is the one side of the square garden
therefore
4(5) = 20 m is the perimeter of the garden
:
Overall dimensions: 5+2 and 5+1, therefore
7 * 6 =42 sq/m is the area of the garden and the path
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