Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

You have 116 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.

Sagot :

jzakoian
Let us call X the length of the rectangle and x the width if it.
Perimeter is 2X+2x so we have 2X+2x=116.
Which means X=(116-2x)/2 which means X=58-x
Surface (S) is X*x
So we can deduce:
S=X*x
S=(58-x)*x
S=58x-[tex] x^{2} [/tex]

We are looking to maximise.
This happens when the derivate equals 0
Derivate is 58-2x
58-2x=0 if x=29

So the surface is maximized when x=29
Which means X=29 as well (X=58-x)

Got it?

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.