SOLUTION: A building's length 10meters less than twice its width.the sidewalk around the building is 2meters wide and the area of the sidewalk alone is 216square meters.find the length of th
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Question 968764: A building's length 10meters less than twice its width.the sidewalk around the building is 2meters wide and the area of the sidewalk alone is 216square meters.find the length of the building Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the area of the sidewalk is equal to the area of the building plus the sidewalk minus the area of the building.
the area of the sidewalk is given as 216.
A1 = area of the building.
A2 = area of the building plus the sidewalk.
A2 - A1 = 216.
L = length of the building
W = wisth of the building.
the sidewalk is 2 meters wide.
the length of the building plus the width of the sidewalk on both sides is equal to L + 4.
the width of the building plus the width of the sidewalk on both sides is equal to W + 4.
we have:
A1 = L * W
A2 = (L+4) * (W + 4)
we know that A2 - A1 is equal to 216 because that's the area of the sidewalk and the area of the sidewalk was given as 216 square meters.
area of the sidewalk byh itself is therefore equal to A2 - A1 which is equal to (L+4) * (W+4) - L*W.
Simplify this equation to get:
LW + 4W + 4L + 16 - LW = 216.
combine like terms to get 4W + 4L + 16 = 216
subtract 16 from both sides of the equation to get 4W + 4L = 200.
you are given that the length of the building is equal to 10 meters less than two times the width of the building.
the formula for that is L = 2W - 10.
in the equation of 4W + 4L = 216, replace L with 2W - 10 to get 4W + 4(2W-10) = 200
simplify to get 4W + 8W - 40 = 200
combine like terms to get 12W - 40 = 200
add 40 to both sides of the equation to get 12W = 240
divide both sides of the equation by 2 to get W = 20.
if W = 20, then L = 2W - 10 = 2(20) - 10 = 30.
you have W = 20 and L = 30.
that's your solution.
the diagram shown below shows what this looks like:
