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A park is [tex]25 \frac{4}{5} \, \text{m}[/tex] long and [tex]20 \frac{2}{3} \, \text{m}[/tex] wide.

1. Find the perimeter of the park.
2. If a walkway is to be constructed inside the park that is [tex]2 \frac{3}{8} \, \text{m}[/tex] wide, what would be the inside perimeter of the walkway?

Sagot :

GinnyAnswer
Sure, let's solve this problem step-by-step:

1. Determine the dimensions of the park:
- The length of the park is [tex]\( 25 \frac{4}{5} \)[/tex] meters.
- The width of the park is [tex]\( 20 \frac{2}{3} \)[/tex] meters.

2. Convert mixed numbers to improper fractions (or decimal numbers for easier calculation):
- Length: [tex]\( 25 \frac{4}{5} \approx 25.8 \)[/tex] meters (since [tex]\( 4/5 = 0.8 \)[/tex])
- Width: [tex]\( 20 \frac{2}{3} \approx 20.666666666666668 \)[/tex] meters (since [tex]\( 2/3 \approx 0.6666666666666666 \)[/tex])

3. Calculate the perimeter of the park:
The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is [tex]\( P = 2 \times ( \text{Length} + \text{Width} ) \)[/tex].
- [tex]\( \text{Perimeter of the park} = 2 \times (25.8 + 20.666666666666668) = 92.93333333333334 \)[/tex] meters

4. Determine the width of the walkway:
- The walkway width is [tex]\( 2 \frac{3}{8} \)[/tex] meters.

5. Convert this mixed number to a decimal:
- Walkway width: [tex]\( 2 \frac{3}{8} = 2 + \frac{3}{8} = 2.375 \)[/tex] meters

6. Calculate the new dimensions of the inside walkway:
- The walkway runs along the inside of the park, reducing both the length and the width by twice the walkway width (since the walkway takes up space on both sides of the length and width).
- New Length: [tex]\( 25.8 - 2 \times 2.375 = 25.8 - 4.75 = 21.05 \)[/tex] meters
- New Width: [tex]\( 20.666666666666668 - 2 \times 2.375 = 20.666666666666668 - 4.75 = 15.916666666666668 \)[/tex] meters

7. Calculate the perimeter of the inside walkway:
- [tex]\( \text{Perimeter of the inside walkway} = 2 \times (21.05 + 15.916666666666668) = 73.93333333333334 \)[/tex] meters

Summarizing the solution:
- The perimeter of the park is approximately 92.93 meters.
- The perimeter of the inside walkway is approximately 73.93 meters.
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