Question 343497: I cannot figure out how to set up an equation to find the length and the width of the rectange. The word problem is:
The perimeter of a rectangle is 32 inches, and the area is 60 square inches. Find the length and width of the rectangle.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The perimeter of a rectangle is 32 inches, and the area is 60 square inches.
Find the length and width of the rectangle.
:
Start with the perimeter equation
2L + 2W = 32
Simplify, divide by 2
L + W = 16
W = (16-L); use this form for substitution
:
The area equation
L * W = 60
Replace W with (16-L)
L*(16-L) = 60
16L - L^2 = 60
Arrange as a quadratic equation
-L^2 + 16L - 60 = 0
Factors easier if we change the signs, mult by -1
L^2 - 16L + 60 = 0
Factors to
(L-6)(L-10) = 0
Two solutions
L = 10, then W=6
or
L = 6, then W=10
:
:
You can confirm this by finding the perimeter and area when L=10, W=6
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