Question

A training field is formed by joining a rectangle and two semicircle. The rectangle is 87m long and 64m wide. What is the length of a training track running around the field? ( Use the value 3.14 pie, and do not round your answer. Be sure to include the correct unit in your answer.)

Answer 1

The legth of running around this track will be the length of both semi-circles plus the two bigger sidesof the rectangle.

The length of a semi -circle is half the length of a circle, and can be expressed as:

`S=(2\pi r)/(2)=\pi r`

Where r is the radius of the semi-circle. The diameter of the semi-circles is the same as the smaller sides of the rectangle and its radius is half the diameter, so:

`r=(d)/(2)=(64)/(2)=32`

So, the total length, as said above, is the sum of the length of both semi-circles plus two times the bigger side:

`\begin{gathered} L=2S+2w \\ L=2\cdot\pi r+2\cdot87 \\ L=2\cdot3.14\cdot32+2\cdot87 \\ L=200.96+174 \\ L=374.96 \end{gathered}`

Al the measures used were in meters and length is given in meters to the first power, so the unit of the result is also meters, or just "m".

Thus the answer is 374.96 m.