Question

The diagram shows a track composed of a rectangle with a semicircle on each end. The area of the rectangle is 14,400 square meters. What is the perimeter of the​ track?

Answer 1

`90pi+320`

Explanation:

The perimeter of the track is the two circumferences of the semicircles (when combined, they form one circle, so we can just find the circumference of the circle) added to the lengths of the rectangle (`160` meters).

To find the circumference of the circle, we need to know the diameter.

Circumference of a circle: `dpi` or `2rpi`, where `d` represents diameter and `r` represents radius

The diameter of the circle happens to be the same as the width of the rectangle. We know that the area of a rectangle is found by multiplying its length by its width. We know that the area is `14400` and that its length is `160`.

Width: area divided by length

`14400/160=90`

The diameter of the circle and the width of the rectangle is `90` meters.

Circumference:

`90*pi=90pi rarr` If you are using an approximation such as 3.14 for `pi`, multiply that by 90

Add `160*2` to the circumference since the lengths of the rectangle are also part of the perimeter.

`160*2=320`

`90pi+320`