Question 750749: A square yard has a 6-foot wide sidewalk around a square lawn. the sides of the yard, including the sidewalk, have length y. evaluate for y=70, the polynomial that gives the area of the sidewalk.
I have driven myself in circles on this problem. i originally found the area of the sidewalk to be 420 by multiplying 6*70 but upon further evaluation concluded that was incorrect by finding the area of the yard (70*70) to be 4900 and the area of the lawn (64*64) to be 4096 making the sidewalk take up 804 sqft of space. I am to a point where im thoroughly confused.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! A square yard has a 6-foot wide sidewalk around a square lawn. the sides of the yard, including the sidewalk, have length y. evaluate for y=70, the polynomial that gives the area of the sidewalk.
the area of the square including the sidewalk is y^2
the area of the sidewalk is y^2 - (y-12)^2
y^2 - (y^2 -24y +144)
y^2 -y^2 +24y -144
we are left with
24y - 144 = 24*70 -144 = 1536
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