Question

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

Answer 1

Solution:

$2L+4w=800$

so $L=400-2w$

$A=L*w$

$A=(400-2w)w$

$A=-2w^2+400w$

$\dfrac{dA}{dw}=0 \;$

$=-4w+400$

$w=100$

$L=400-200=200$

Answer:

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