Question 1150605: A 8 yard by 10 yard swimming pool is surrounded by a deck of uniform width.the area of the deck is 72yd squared . Find the width of the deck Found 2 solutions by Alan3354, ikleyn:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! A 8 yard by 10 yard swimming pool is surrounded by a deck of uniform width.the area of the deck is 72yd squared . Find the width of the deck
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d = deck width
Area of pool & deck = (2d+8)*(2d+10)
Area of deck = (2d+8)*(2d+10) - 8*10 = 72
The area of 72 square yards is the difference of the area of the larger rectangle and the pool's area.
Let w be the uniform width of the deck.
Then the dimensions of the larger rectangle are (8+2w) yards and (10+2w) yards,
and its area is (8+2w)*(10+2w).
Thus you have this equation
(8+2w)*(10+2w) = 8*10 + 72.
Simplify it
80 + 20w + 16w + 4w^2 = 80 + 72
4w^2 + 36w - 72 = 0
w^2 + 9w - 18 = 0
= = .
Only positive root makes sense w = = 1.685 yards. ANSWERCHECK. (8+2*1.685)*(10+2*1.685) - 8*10 = 72.0169 very close to 72 square yards. ! Correct !
