I've been really struggling to figure out this question.
"The total enclosure around the playground at a daycare is to be $800$ square feet. One side of the playground is bordered by the school building while the three remaining sides will be enclosed with fencing.Find the dimensions that minimze the amount of fencing needed.
The answers I got were width=$\sqrt{300}$ and length = $\frac{\sqrt{40}}6$. When I checked if they were right by multiplying width by height, I didn't get $800$, so I think it's wrong.
What can I do to solve this question? Thanks.
The question implies that the enclosure is a rectangle. Suppose the side length parallel to the school building's face is $h$, then the other side length is $\frac{800}h$ and we want to minimise $h+\frac{1600}h$.
The derivative of this is $1-\frac{1600}{h^2}$ and this is zero when $h=40$. Thus the enclosure should be $40$ feet long across the building face and $20$ feet wide to minimise the fencing (which will be $80$ feet in this case).