# Maximum Area-Calculus-Edit

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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 -

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 -

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 -

THANK YOU SO MUCH! I got 250 for each dimension :)

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