SOLUTION: A rectangular building that measures 100m by 80m is to be surrounded by a lawn of uniform width. The area of the lawn must be equal the area of the building. Find the width of the

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Question 199699: A rectangular building that measures 100m by 80m is to be surrounded by a lawn of uniform width. The area of the lawn must be equal the area of the building. Find the width of the lawn, to the nearest tenth of a metre.
Thanks soo much.. exam tomorrow =(
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
area of building is 80m * 100m or 8000m^2

let x = "width of lawn"
so dimensions of building plus lawn are 80+2x by 100+2x

since the area of the lawn equals the area of the building,
(80+2x)(100+2x) = 2 * 8000

FOILing ___ 8000 + 360x + 4x^2 = 16000

subtracting 16000 and dividing by 4 ___ x^2 + 90x - 2000 = 0

use quadratic formula to find x