Question

An indoor track is made up of a rectangular region with two semi-circles at the ends. The distance

around the track is 400 meters. Determine the radius of the semicircular ends of the track in terms of y.

Answer 1

r = (200 - y)/π

Explanation:

The question details includes;

The shape of the indoor track = Two semi-circular ends and a mid rectangular region

The distance around the indoor track = 400 meters

The radius, r, of the semicircular ends in terms of y = Required

Let y represent the length of the rectangular middle area of the track, we have;

The perimeter of the indoor track = The distance around the track = 400 m

The perimeter of the indoor track = 2 × π·r + 2 × y = 400

2 × (π·r + y) = 400

∴ π·r + y = 400/2 = 200

r = (200 - y)/π