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Let the width of the pool = W and the length of the pool = L. We are told that the length is greater than W so
Assume the three sides that are fenced in are the two widths and one length, and that's with 60 yards of fencing. Thus,
We also know that the area of the pool = 352. So,
from both sides of (1) to get
Replace L with
in (2) to get
by W and we get
So, (3) becomes
This is a quadratic equation which can also be written as
We divide both sides by 2 and get
The coefficients of this quadratic equation are -1, 30, and -176.
Remember the quadratic equation, solving for w:
Replace a, b, and c with -1, 30, and -176 respectively and you get
Multiply things out and you get
So, W can equal
which = 8
or W can equal
which = 22
From (1) we know that
. If W = 8 then
If W = 22 then
. But, L must be > W and 16 is not > 22 so W = 22 is not a solution.
So, L = 44. and from (1) we know that
To verify our answer, that
we plug these values into (1) and (2):
should = 60 and it does.
should = 352 and it does.