Posted by **Lisa** on Sunday, March 10, 2013 at 9:09pm.

We have 900 ft of fencing and we want to construct a back yard. If we are using the building as part of the barrier for the yard what are the dimensions that allow maximum area?

I am not even sure how to start though I know I am supposed to calculate the derivative of the setup. Thank you

Here is the image. imgur F5NJVqp

- Maximum Area-Calculus-Edit -
**Damon**, Sunday, March 10, 2013 at 9:26pm
perimeter = 2 W + L = 900

so

L = (900 - 2W)

A = W L

A = W (900 -2W)

A = 900 W - 2 W^2

now you can complete the square for the parabola and find the vertex or you can use calculus

dA/dW = 0 for max = 900 - 4 W

W = 225

900 = 2 W + L

900 = 450 + L

L = 450

glad you learned calculus and did not have to find the vertex of that parabola? :)

- Maximum Area-Calculus-Edit -
**Damon**, Sunday, March 10, 2013 at 9:37pm
Oh, although I can not see your image I see your note on your earlier question answered by Steve.

If only 100 feet of the building is used then

2 W + L + (L-100) = 900

2 W + 2 L - 100 = 900

2 W + 2 L = 1000

then continue as before

- Maximum Area-Calculus-Edit -
**Lisa**, Sunday, March 10, 2013 at 10:08pm
THANK YOU SO MUCH! I got 250 for each dimension :)

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