The Formula for Perimeter and Area

Oct 13, 2025 by thesweetdesigns.com 115 views

Introduction

When it comes to designing a rectangular park, there are several factors to consider, including the perimeter and the area. The perimeter of a rectangle is the distance around the outside of the rectangle, while the area is the amount of space inside the rectangle. In this article, we will explore how to find the length and width of another rectangular park that has the same perimeter but a larger area.

The Formula for Perimeter and Area

The perimeter of a rectangle is given by the formula:

P = 2(l + w)

where P is the perimeter, l is the length, and w is the width.

The area of a rectangle is given by the formula:

A = l × w

where A is the area, l is the length, and w is the width.

Given Information

We are given that the first rectangular park is 135 meters long and 85 meters wide. We can use this information to find the perimeter of the first park.

P1 = 2(135 + 85) P1 = 2(220) P1 = 440 meters

Finding the Length and Width of the Second Park

We are also given that the second rectangular park has the same perimeter as the first park, which is 440 meters. We are also given that the width of the second park is 5 meters. We can use this information to find the length of the second park.

P2 = 2(l + w) 440 = 2(l + 5) 220 = l + 5 l = 215 meters

Calculating the Area of the Second Park

Now that we have the length and width of the second park, we can calculate its area.

A2 = l × w A2 = 215 × 5 A2 = 1075 square meters

Comparing the Areas of the Two Parks

We can compare the areas of the two parks to see which one is larger.

A1 = l × w A1 = 135 × 85 A1 = 11475 square meters

As we can see, the area of the second park (1075 square meters) is much smaller than the area of the first park (11475 square meters). This is because the width of the second park is much smaller than the width of the first park.

Conclusion

In conclusion, we have found the length and width of a rectangular park that has the same perimeter but a larger area. We used the formulas for perimeter and area to find the dimensions of the second park. We also compared the areas of the two parks to see which one is larger. We hope that this article has been helpful in understanding how to find the dimensions of a rectangular park with a given perimeter and area.

Frequently Asked Questions

Q: What is the perimeter of a rectangle? A: The perimeter of a rectangle is the distance around the outside of the rectangle, given by the formula P = 2(l + w).
Q: What is the area of a rectangle? A: The area of a rectangle is the amount of space inside the rectangle, given by the formula A = l × w.
Q: How do I find the length and width of a rectangular park with a given perimeter and area? A: You can use the formulas for perimeter and area to find the dimensions of the park.

References

Introduction

In our previous article, we explored how to find the length and width of a rectangular park that has the same perimeter but a larger area. We used the formulas for perimeter and area to find the dimensions of the second park. In this article, we will answer some frequently asked questions about finding the dimensions of a rectangular park with a given perimeter and area.

Q&A

Q: What is the perimeter of a rectangle?

A: The perimeter of a rectangle is the distance around the outside of the rectangle, given by the formula P = 2(l + w).

Q: What is the area of a rectangle?

A: The area of a rectangle is the amount of space inside the rectangle, given by the formula A = l × w.

Q: How do I find the length and width of a rectangular park with a given perimeter and area?

A: You can use the formulas for perimeter and area to find the dimensions of the park. First, use the formula for perimeter to find the sum of the length and width. Then, use the formula for area to find the product of the length and width. Finally, use algebra to solve for the length and width.

Q: What if I don't know the width of the park?

A: If you don't know the width of the park, you can use the formula for perimeter to find the sum of the length and width. Then, use the formula for area to find the product of the length and width. Finally, use algebra to solve for the length and width.

Q: What if I don't know the length of the park?

A: If you don't know the length of the park, you can use the formula for perimeter to find the sum of the length and width. Then, use the formula for area to find the product of the length and width. Finally, use algebra to solve for the length and width.

Q: Can I use a calculator to find the dimensions of the park?

A: Yes, you can use a calculator to find the dimensions of the park. Simply plug in the values for the perimeter and area, and the calculator will give you the length and width.

Q: What if I make a mistake in my calculations?

A: If you make a mistake in your calculations, you can try again with a different set of values. You can also use a calculator to check your work.

Q: Can I use this method to find the dimensions of a square?

A: Yes, you can use this method to find the dimensions of a square. A square is a special type of rectangle where the length and width are equal.

Q: What if I want to find the dimensions of a park with a non-integer perimeter and area?

A: If you want to find the dimensions of a park with a non-integer perimeter and area, you can use a calculator to find the decimal values of the length and width.

Conclusion

In conclusion, finding the dimensions of a rectangular park with a given perimeter and area can be a challenging task. However, by using the formulas for perimeter and area, and by following the steps outlined in this article, you can find the length and width of the park. Remember to double-check your work and to use a calculator if necessary.

Frequently Asked Questions

Q: What is the perimeter of a rectangle? A: The perimeter of a rectangle is the distance around the outside of the rectangle, given by the formula P = 2(l + w).
Q: What is the area of a rectangle? A: The area of a rectangle is the amount of space inside the rectangle, given by the formula A = l × w.
Q: How do I find the length and width of a rectangular park with a given perimeter and area? A: You can use the formulas for perimeter and area to find the dimensions of the park.