Question

A training field is formed by joining a rectangle and to semicides, as shown below. The rectangle is 82 m long and 50 m wide. What is the length of a trainingtrack running around the field? (use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer)

Answer 1

To solve the exercise we need to know the perimeter of the circle

`\begin{gathered} L_c=2\cdot\pi\cdot r \\ d=2\cdot r \\ L_c=\pi\cdot d \end{gathered}`

From the exercise we know that there are 2 lengths of 82m and the diameter of the semicircle is 50, so we generate our equation. Since we have 2 semicircles with the same diameter, then the corridor is as if it ran a complete circle.

`\begin{gathered} L_f\to\text{Lenght of the training field} \\ d\to\text{diameter} \\ l\to\text{length of the rectangle} \\ L_c\to\text{perimeter of the circle} \end{gathered}`
`L_f=2l+L_c`
`\begin{gathered} l=82m \\ d=50m \\ \pi=3.14 \\ L_c=50\mleft(3.14\mright)m \\ L_c=157m \end{gathered}`
`\begin{gathered} L_f=2(82)+157 \\ L_f=164+157 \\ L_f=321m \end{gathered}`

The runner will run 321.0 m in the training field