SOLUTION: An architect has designed a motel pool within a rectangular area that is fenced on three sides. If she uses 60 yards of fencing to enclose an area of 352 square yards, then what ar

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Question 68515This question is from textbook
: An architect has designed a motel pool within a rectangular area that is fenced on three sides. If she uses 60 yards of fencing to enclose an area of 352 square yards, then what are the dimensions of the fence. (L and W) Assume L is greater than W. This question is from textbook

Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
l+%2B+2w+=+60
lw+=+352
w+=+352%2Fl
l+%2B+2%28352%2Fl%29+=+60
l+%2B+%28704+%2F+l%29+=+60
l%5E2+%2B+704+=+60l
l%5E2+-+60l+%2B+704+=+0
l+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
l+=+%2860+%2B-+sqrt%28+3600-4%2A704+%29%29%2F+2+
l+=+%2860+%2B-+sqrt%28784%29%29%2F+2+
l+=+%2860+%2B-+28%29+%2F+2
1st try the + sqrt
l+=+%2860+%2B+28%29+%2F+2
l+=+44 answer
w+=+352+%2F+44
w+=+8 answer
check
lw+=+352
44%2A8+=+352
352+=+352
OK
l+%2B+2w+=+60
44+%2B+16+=+60
60+=+60
OK
If I chose the -sqrt of 784, which was -28
l+=+%2860+-+28%29+%2F+2
l+=+32%2F2
l+=+16
w+=+352+%2F+16
w+=+22
The length ends up being shorter than the width,
which was not allowed by the problem. These numbers
will still give you the right area and length of
fencing, however.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An architect has designed a motel pool within a rectangular area that is fenced on three sides. If she uses 60 yards of fencing to enclose an area of 352 square yards, then what are the dimensions of the fence. (L and W) Assume L is greater than W.
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Draw the picture of a rectangular area with a motel on one side.
Let the 3-sided fence have perimeter = 2(width)+(length)= 60
and Area = (length)(width)=352 sq yds.
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EQUATIONS:
L+2W=60
L=60-2W
Area=LW=(60-2W)W=352
-2W^2+60W=352
w^2-30w+176=0
(W-22)(W-8)=0
W=8 yds. (if L is to be greater than W).
L=60-2W =60-16 =44 yrds
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Cheers,
Stan H.