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!

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) (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

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Answer by stanbon(75887) (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
-----------------------
Cheers,
Stan H.
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