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Question

Bscally i can show that the best rectangle to get the most area from same perimeter is square.also trying to find one that i can use to apply to all shapes (to decgon wil do) to show that the regular ones get the biggest area for the same perimeter and iv got something below that ur spsd to b able to use on other shapes PLZ SHOW HOW.

(Rectangle)
Perimeter=P let a Length=X Then a width is 1/2(P-2X)

Area= X ((1/2 (P-2X)
= X ( P/2-X)
= PX/2-X^2

HERE IS THE IMPORTANT BIT BELOW PLZ HELP!!!!!!

dA/dx = P/2 - 2x = 0 for max or min <<<<< So 2x = P/2 and x = P/4. - I understand how to get from the above but i dont understand the dA/dx thing

please explain, iv luked at some others and they talk about derivates or something and going from 100-2X to 100X-X^2 + C where C is a constant.

But i dont understand how theyve got to there and how on example earlier they got to that either.

ALL HELP GR8ly APPRECIATED

Answer 1

It seems to me that you have not learned calculus yet but someone tried to help you on this problem with calculus. Well, it is not that easy to explain to you how calculus works in a few words. Fortunately, this problem can be solved without using calculus.

Start from your formula for area:
Area = PX/2-X^2
= P^2/16 - P^2/16 + PX/2 - X^2
= P^2/16 - (P^2/16 - 2*PX/4 + X^2)
= P^2/16 - (X - P/4)^2
Clearly, (X - P/4)^2 is a square and thus is greater than or equal to zero. Area is maximized only when (X - P/4)^2 is zero, that is, the maximum of area is P^2/16 when X = P/4 (answer)

Answer 2

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