SOLUTION: How do I solve for the sides of a rectangle when given only the perimeter (40 feet) and the square feet (90 sq. ft)? Thank you!

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Question 708486: How do I solve for the sides of a rectangle when given only the perimeter (40 feet) and the square feet (90 sq. ft)? Thank you!
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the width and represent the length.

The perimeter of a rectangle is given by

So we know that which is to say , or, better for our purposes,

The area of a rectangle is the length times the width, so:



Putting the quadratic into standard form:



Solve the quadratic for . Discard the value that produces a negative result when you calculate . Note: This quadratic DOES NOT factor over the rationals. Use the quadratic formula, but leave your answer in simplest radical form.

John

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Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do I solve for the sides of a rectangle when given only the perimeter (40 feet) and the square feet (90 sq. ft)?
-----------------------------------
P = 2(L+W)
40 = 2(L+W)
L + W = 20
L = (20-W)
--------------------
A = LW
90 = (20-W)W
-W^2 +20W = 90
-----
W^2 -20W + 90 = 0
W = 13.16
-----
L = 20-W = 6.84
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Cheers,
Stan H.
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