SOLUTION: A sidewalk of uniform width surrounds a rectangular building. How wide is the sidewalk if the building is ten feet longer than wide; if the outside perimeter of the sidewalk is 192

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Question 584498: A sidewalk of uniform width surrounds a rectangular building. How wide is the sidewalk if the building is ten feet longer than wide; if the outside perimeter of the sidewalk is 192 feet, and if the area of the sidewalk is 704 square feet? Please make it a trinomial. I know the answer is 4, just not how to get there algebraically.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"the building is ten feet longer than wide" ___ so the perimeter of the sidewalk will be also

2x + 2(x + 10) = 192 ___ 4x + 20 = 192 ___ x = 43, x + 10 = 53

area of building plus sidewalk ___ 43 * 53

area of sidewalk ___ 704

area of building ___ (43 - 2w)(53 - 2w) where w is the width of the sidewalk

(43 * 53) - 704 = (43 - 2w)(53 - 2w) ___ 4w^2 - 192w - (43 * 53) + 704 = 0