SOLUTION: A square lawn is surrounded by a walk one metre wide. If the area of the walk is equal to half the area of the lawn,what are the dimensions of the lawn???

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Question 132621: A square lawn is surrounded by a walk one metre wide. If the area of the walk is equal to half the area of the lawn,what are the dimensions of the lawn???
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
LET X BE THE LAWN SIDE MEASUREMENT.
X^2=THE LAWN AREA.
(X+2)^2-X^2=X^2/2 TOTAL AREA [(X+2)^2] MINUS THE LAWN AREA [X^2] = 1/2 THE LAWN AREA [X^2/2].
X^2+4X+4-X^2=X^2/2
4X+4=X^2/2
X^2=2(4X+4)
X^2=8X+8
X^2-8X-8=0
USING THE QUADRATIC EQUATION: WE GET:
X=(8+-SQRT[-8^2-4*1*-8])/2*1
X=(8+-SQRT64+32])/2
X=(8+-SQRT96)/2
X=(8+-9.7979)/2
X=(8+9.7979)/2
X=17.7979/2
X=8.899 METERS FOR THE DIMENSION OF THE SQUARE.
PROOF:
(8.899+2)^2-8.899^2=8.899^2/2
10.899^2-79.192=79.192/2
118.788-79.192=39.596
39.596=39.596