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?

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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?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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@ means plus or minus by the way
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)
I once I go to my area formula since I found x I can write Area has a function of r

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

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