Question 266830: the perimetere of a rectangle is 20 in and the area is 16sq in. find the diminsions
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! the perimeter of a rectangle is 20 in
2L + 2W = 20
Simplify, divide by 2
L + W = 10
W = (10-L); this form for substitution
:
and the area is 16sq in.
L * W = 16
Replace W with (10-L)
L * (10-L) = 16
-L^2 + 10L - 16 = 0; our old friend, the quadratic equation
Multiply by -1, change the signs, makes it easier to factor
L^2 - 10L + 16 = 0
Factor
(L-8)(L-2) = 0
Two solutions
L = 8; then W = 2
L = 2: then W = 8
:
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Check solution in perimeter equation
2(8) + 2(2) = 20
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find the dimensions: 8 in by 2 in
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