A rectangular field x units long is capped by a semicircle of radius r at the two ends. The field is to be bounded by a 400-m racetrack.
Express the area of the rectangle as a function of r. I have gotten to x=(-1600@4*sqrt(160000+8r^2))/(16). Do you think I'm headed in the right direction?

Question

A rectangular field x units long is capped by a semicircle of radius r at the two ends. The field is to be bounded by a 400-m racetrack.  
Express the area of the rectangle as a function of r. I have gotten to x=(-1600@4*sqrt(160000+8r^2))/(16). Do you think I'm headed in the right direction?

myininaya · Answer

@ means plus or minus by the way

myininaya · Answer

so I started out with the area of the rectangle =x(r^2-x^2) and the perimeter is 400=2x+2sqrt(r^2-x^2)

myininaya · Answer

I once I go to my area formula since I found x I can write Area has a function of r

myininaya · Answer

I'm assuming cap means the rectangle is enclosed in the semicircle correct?