dimensions of track enclosing largest infield area

[yummymummy1713]

A 400 meter long running track is to be constructed with 2 parallel straight aways of length s joining 2 semi-circular curves of radius r. What are the dimensions of the track that will enclose the largest infield area?

I drew a diagram with 2 parallel lines and 2 semi circles. Therefore part of the equation will be 2s + 2r, right?

If not can you explain, if so what should I do next?

Thanks

 

[stapel]

You have an area with two "flat" sides and two "round" sides, something like:

   =========
 /           \
(             )
 \           /
   =========

The flat sides have length "s". What are the lengths of the round sides? (Hint: The lengths are NOT "r".)

Eliz.

 

[skeeter]

I drew a diagram with 2 parallel lines and 2 semi circles. Therefore part of the equation will be 2s + 2r, right?

2r is not the length of the circular part of the track.

the equation for the track's length would be 2s + 2pi*r = 400

the equation for the infield area would be A = 2rs + pi*r²