Answer to Question #154206 in Calculus for Phyroe

Question #154206

a rectangular field is to be emclosed by a fence and divided into three lots by fences parallel to one of the sides. find the dimensions of the largest field that can be enclosed with 800 feet of fencing


1
Expert's answer
2021-01-08T11:40:17-0500

Solution:

2L+4w=8002L+4w=800

so L=4002wL=400-2w


A=LwA=L*w

A=(4002w)wA=(400-2w)w

A=2w2+400wA=-2w^2+400w

dAdw=0  \dfrac{dA}{dw}=0 \;

=4w+400=-4w+400

w=100w=100

L=400200=200L=400-200=200


Answer:

Dimensions of the largest field that can be enclosed with 800 feet of fencing are 200, 100.

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