Question

60. An athletic field is a 100 yd-by-40 yd rectangle with asemicircle at each of the short sides. A running track 10 ydwide surrounds the field. Find the perimeter of the outsideof the running track to the nearest tenth of a yard.

Answer 1

The perimeter of the outside of the running track is the sum of the lengths A, B, C, and D.

Notice that A=B=100 yd, and D=C.

To find D we compute the semi perimeter of a circle with radius:

`r_D=(40yd)/(2)+10yd=30yd\text{.}`

Then:

`D=(1)/(2)\pi\cdot2r_D=\pi r_D=30\pi yd\text{.}`

Therefore the perimeter of the outside of the running track is:

`A+B+C+D=(60\pi+200)yd\text{.}`

Answer: 388.5yd.