SOLUTION: Perimeter of a rectangle is 32 inches, area of the rectangle is 60 square inches. What is the length and width?

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Question 193054: Perimeter of a rectangle is 32 inches, area of the rectangle is 60 square inches. What is the length and width?
Answer by jonvaliente(64) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter=2*L + 2*W
Area = L*W
Let L=length and W=width of your rectangle
If Perimeter=32, then
2*L+2*W=32 (1)
If Area=60, then
L*W=60 (2)
Let's take (1), and express L in terms of W:
2L + 2W = 32
L + W = 16 (divide bot sides by 2)
L = 16-W (subtract W from both sides)
We can now substitute this value of L in (2), so:
%2816-W%29%2AW=60
16W-W%5E2=60 (Simplifying)
W%5E2-16W%2B60=0 (Add W^2-16W on both sides)
%28W-6%29%28W-10%29=0 (Factoring)
If we take W-6=0,
W=6 and L=16-W=16-6=10 inches, so our rectangle is 6 inches wide and 10 inches long
If we take W-10=0
W=10 and L=16-10=6 inches, but generally length is longer than width so we just take the first solution.