Question 988686: Find the dimensions of a rectangle whose area is 182 cm2 and whose perimeter is 54 cm. (Enter your answers as a comma-separated list.)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Find the dimensions of a rectangle whose area is 182 cm2 and whose perimeter is 54 cm. (Enter your answers as a comma-separated list.)
Let L = the length
Let W = the width
:
The perimeter
2L + 2W = 54
simplify divide by 2
L + W = 27
W = (27-L), use this form for substitution
:
The area
L * W = 182
Replace W with (27-L)
L(27-L) = 182
27L - L^2 = 182
a quadratic equation
-L^2 + 27L - 182 = 0
Factor easier if we multiply by -1 and change the signs
L^2 - 27L + 182 = 0
you can use the quadratic formula here, but this will factor to
(L-14)(L-13) = 0
Two solutions
L = 14, W = 13
or
L = 13, W = 14
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:
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Confirm this
2(14) + 2(13) = 54
14 * 13 = 182
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