Question
A high school track is shaped as a rectangle with a half circle on either side.
A rectangle has a length of 85 yards and width of 25 yards. 2 semicircles with diameters of 25 yards are on each end of the rectangle.
Jasmine plans on running three laps. How many yards will Jasmine run? Use 3.14 for Pi.
248.5 yd
490.5 yd
725.5 yd
745.5 yd
A rectangle has a length of 85 yards and width of 25 yards. 2 semicircles with diameters of 25 yards are on each end of the rectangle.
Jasmine plans on running three laps. How many yards will Jasmine run? Use 3.14 for Pi.
248.5 yd
490.5 yd
725.5 yd
745.5 yd
Answers
Answered by
GPT-4o mini
To find the total distance that Jasmine will run in three laps around the track, we need to first calculate the perimeter of the track.
The track consists of a rectangle with two semicircles on each end.
1. **Calculate the perimeter of the rectangle part:**
- The length of the rectangle is 85 yards, and the width is 25 yards.
- The two sides of the rectangle that contribute to the perimeter are 85 yards each, while the two widths (which are not included because they are replaced by semicircles) do not contribute directly to the perimeter.
\[
\text{Perimeter of rectangle part} = 2 \times \text{length} = 2 \times 85 = 170 \text{ yards}
\]
2. **Calculate the circumference of the two semicircles:**
- The diameter of each semicircle is 25 yards, which means the radius is \( \frac{25}{2} = 12.5 \) yards.
- The formula for the circumference of a full circle is \( C = 2\pi r \). For one semicircle, it would be half of that:
\[
\text{Circumference of one semicircle} = \pi r = 3.14 \times 12.5
\]
\[
\text{Circumference of one semicircle} = 39.25 \text{ yards}
\]
Since there are two semicircles:
\[
\text{Circumference of two semicircles} = 2 \times 39.25 = 78.5 \text{ yards}
\]
3. **Calculate the total perimeter of the track:**
\[
\text{Total perimeter} = \text{Perimeter of rectangle part} + \text{Circumference of two semicircles}
\]
\[
\text{Total perimeter} = 170 + 78.5 = 248.5 \text{ yards}
\]
4. **Calculate the distance Jasmine will run for three laps:**
\[
\text{Distance for three laps} = 3 \times 248.5 = 745.5 \text{ yards}
\]
Thus, the total distance Jasmine will run is **745.5 yards**. Therefore, the answer is **745.5 yd**.
The track consists of a rectangle with two semicircles on each end.
1. **Calculate the perimeter of the rectangle part:**
- The length of the rectangle is 85 yards, and the width is 25 yards.
- The two sides of the rectangle that contribute to the perimeter are 85 yards each, while the two widths (which are not included because they are replaced by semicircles) do not contribute directly to the perimeter.
\[
\text{Perimeter of rectangle part} = 2 \times \text{length} = 2 \times 85 = 170 \text{ yards}
\]
2. **Calculate the circumference of the two semicircles:**
- The diameter of each semicircle is 25 yards, which means the radius is \( \frac{25}{2} = 12.5 \) yards.
- The formula for the circumference of a full circle is \( C = 2\pi r \). For one semicircle, it would be half of that:
\[
\text{Circumference of one semicircle} = \pi r = 3.14 \times 12.5
\]
\[
\text{Circumference of one semicircle} = 39.25 \text{ yards}
\]
Since there are two semicircles:
\[
\text{Circumference of two semicircles} = 2 \times 39.25 = 78.5 \text{ yards}
\]
3. **Calculate the total perimeter of the track:**
\[
\text{Total perimeter} = \text{Perimeter of rectangle part} + \text{Circumference of two semicircles}
\]
\[
\text{Total perimeter} = 170 + 78.5 = 248.5 \text{ yards}
\]
4. **Calculate the distance Jasmine will run for three laps:**
\[
\text{Distance for three laps} = 3 \times 248.5 = 745.5 \text{ yards}
\]
Thus, the total distance Jasmine will run is **745.5 yards**. Therefore, the answer is **745.5 yd**.