SOLUTION: Ok. I need to find the optimum perimeter for a rectangle with the area of 242cm squared. My teacher didn't even teach us he just gave it to us and said do it. I am in grade 8. I wo

Question 758375: Ok. I need to find the optimum perimeter for a rectangle with the area of 242cm squared. My teacher didn't even teach us he just gave it to us and said do it. I am in grade 8. I would appreciate if you could really expand on this so I can understand. THANKS :D
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
I need to find the optimum perimeter for a rectangle with the area of 242cm squared.
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You can find the minimum perimeter, not sure what optiumum would be.
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Pick a perimeter and find the max area: P = 100
P = 2L + 2W = 100
L + W = 50
L = 50 - W
--------
Area = L*W = W*(50 - W)
Area = 50W - W^2
W^2 - 50W + Area = 0
It's a quadratic in W
Ther vertex is on the Axis of Symmetry which is
W = -b/2a
----
W = 50/2 = 25
L = 25
---> Max area of a rectangle of given perimeter is a square.
========================
For Area = 242
L = W = sqrt(242)
= cm

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