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MATH / A rectangular field is enclosed in an athletic track, as shown below. The track…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A rectangular field is enclosed in an athletic track, as shown below.  The track consists of two edges of the field, and two semicircles.  The length of the track is 400 meters.  What is the largest possible area of the field, in square meters?

[asy]
unitsize(1 cm);

filldraw((0,0)--(3,0)--(3,2)--(0,2)--cycle,lightgreen);
draw((0,0)--(3,0),linewidth(2*bp));
draw((0,2)--(3,2),linewidth(2*bp));
draw(arc((3,1),1,-90,90),linewidth(2*bp));
draw(arc((0,1),1,90,270),linewidth(2*bp));
[/asy]

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
09ca1096-5d67-593a-8594-86dd2d42e8c4
task_key
intermediate~5falgebra--test--09ca1096-5d67-593a-8594-86dd2d42e8c4
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import