SOLUTION: what is the largest possible area of a rectangular with perimeter 10?

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Question 1121334: what is the largest possible area of a rectangular with perimeter 10?
Found 2 solutions by math_helper, solver91311:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
It would be a square, so each side is 10/4 = 2.5, thus the area is 2.5%5E2+=+highlight%28+6.25+%29+ sq units
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Proof (using Calculus):
Let x = length
Then w = width = (10 - 2x) / 2
Area, A, is +A+=+x%2Aw+=+x+%2810-2x%29%2F2+=+5x-x%5E2+
+dA%2Fdx+=+5-2x++
5-2x = 0 —> x = 5/2 = 2.5
Since +dA%5E2%2Fd%5E2x+=+-4%2F2+=+-2+ the curve is concave down so the value is a maximum.
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Without Calculus, you can graph the function and compute values by hand.
+graph%28300%2C300%2C+-5%2C5%2C-5%2C10%2C+grid%281%29%2C+5x-x%5E2%29+

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You can also solve it algebraically by using the fact that the vertex of a parabola expressed as is located at the point .


John

My calculator said it, I believe it, that settles it