# The greatest area for a rectangle on a track field.

An athletic field with a perimeter of 0.25 miles consists of a rectangle with a semicircle at each end, as shown below. Find the dimensions that yield the greatest possible area for the rectangular region.

This is the work that I did below. I was wondering if this was the greatest possible area for the rectangle below.

• Near the end of page $$1$$, you wrote $$r=\frac{2}{16\pi}$$ when you meant to say $$2r=\frac{2}{16\pi}$$
• Once we found out that $$r=\frac{1}{16\pi}$$, we can compute $$l=\frac18 - \pi r= \frac18 -\frac1{16}=\frac1{16}$$ directly without finding $$A$$ explicitly.
• you wrote $r=\frac2{16\pi}$ and then you wrote $w=\frac{1}{8\pi}$? – Siong Thye Goh Dec 11 '18 at 1:53
• Great, do not write $r = \frac1{16\pi} \times 2$, you can write $r \times 2 = \frac1{16\pi} \times 2$ or $2r = \frac1{16\pi} \times 2$. – Siong Thye Goh Dec 11 '18 at 1:56