Question

A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 91 m long and 68 m wide. What is the length of a training track running around the field? (Use the value 3.14 for I, and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

Concept:

To figure out the length of the running track, we will use the following steps below

Step 1:

Calculate the length of the round the two semicircles

`\begin{gathered} perimeter\text{ of semi circle=}\pi r \\ r=(68m)/(2)=34m \end{gathered}`

By substituting the values in the formula above, we will have

`\begin{gathered} Perimeter\text{ of semicircle=}\pi r \\ Perimeter\text{ of semicircle=3.14}*34m \\ Perimeter\text{ of semicircle=106.76m} \end{gathered}`

Step 2:

The image below will be used to calculate the length round the training track

Hence,

To calculate the length of the track we will have

`\begin{gathered} Length\text{ of track=AB+arc BD+DC+arc AC} \\ AB=91m \\ arcBD=106.76m \\ arcAC=106.76m \\ DC=91m \end{gathered}`

By substituting the values, we will have

`\begin{gathered} \begin{equation*} Length\text{ of track=AB+arc BD+DC+arc AC} \end{equation*} \\ Length\text{ of track=91+106.76+91m+106.76} \\ Length\text{ of track=395.52m} \\ Length\text{ of track=395.52m} \end{gathered}`

Hence,

The final answer = 395.52m