Question

A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 82m long and 57m wide. What is the length of a training track running around the field? (Use the value 3.14 for pi)

Answer 1

The length of the training track is calculated by adding the perimeters of the rectangular and semicircular parts of the field, resulting in a total length of 456.98 meters using the value of 3.14 for pi.

Step-by-step explanation:

The student is asking about calculating the perimeter of a training track that includes a rectangle and two semicircles. To get the perimeter of the entire track, we need to add the lengths of all the sides of the rectangle and the circumferences of the semicircles.

The rectangle's sides add up to twice its length plus twice its width, which is 2 × 82m + 2 × 57m. Each semicircle has a diameter equal to the width of the rectangle, so the circumference of a full circle would be π × diameter, then we take half of that for a semicircle. Using 3.14 for π, the circumference of one semicircle is π × 57m divided by 2. We add this circumference twice for both semicircles and combine it with the perimeter of the rectangle to get the total length of the track.

Track length = 2 × 82m + 2 × 57m + 2 × (π × 57m / 2)

This expression simplifies to 164m + 114m + 3.14 × 57m, which equals 278m + 178.98m, giving us a total track length of 456.98m.