Question

a training field is formed by joining a rectangle and two semicircles, as shown below. the rectangle is 92 m long and 61 m wide. what is the length of a training track running around the field? (use the value 3.14 for π, and do not round your answer. be sure to include the correct unit in your answer.)

Explanation:

Step1: Identify the components of the track length

The track length is composed of two lengths of the rectangle and the circumference of a circle (formed by the two - semicircles). The length of the rectangle is \(l = 92\) m and the width of the rectangle (diameter of the circle) is \(d=61\) m.

Step2: Calculate the length of the two straight - parts

The two straight - parts of the track come from the lengths of the rectangle. The total length of the two straight - parts is \(2l\), where \(l = 92\) m. So \(2l=2\times92 = 184\) m.

Step3: Calculate the circumference of the circle

The formula for the circumference of a circle is \(C=\pi d\). Given \(d = 61\) m and \(\pi=3.14\), then \(C = 3.14\times61=191.54\) m.

Step4: Calculate the total length of the track

The total length of the track \(L\) is the sum of the length of the two straight - parts and the circumference of the circle. So \(L=184 + 191.54=375.54\) m.

Answer:

\(375.54\) m