Calculating the Area of Garden A

Oct 13, 2025 by wbrum.org 84 views

Introduction

In this article, we will compare the areas of two rectangular gardens, Garden A and Garden B, to determine which one has the largest area. Both gardens are surrounded by 120 feet of fencing, and we are given the length of one side of each garden. We will use this information to calculate the area of each garden and compare the results.

The Problem

Garden A has one side length of 25 feet, and Garden B has one side length of 50 feet. Both gardens are surrounded by 120 feet of fencing. We need to find the area of each garden and compare the results.

Calculating the Area of Garden A

To calculate the area of Garden A, we need to find the length of the other side of the garden. Since the garden is surrounded by 120 feet of fencing, we can set up an equation to represent the perimeter of the garden:

2(l + w) = 120

where l is the length of the garden and w is the width of the garden. We are given that one side length of the garden is 25 feet, so we can substitute this value into the equation:

2(25 + w) = 120

Simplifying the equation, we get:

50 + 2w = 120

Subtracting 50 from both sides of the equation, we get:

2w = 70

Dividing both sides of the equation by 2, we get:

w = 35

So, the width of Garden A is 35 feet. Now, we can calculate the area of Garden A:

Area = l × w = 25 × 35 = 875 square feet

Calculating the Area of Garden B

To calculate the area of Garden B, we need to find the length of the other side of the garden. Since the garden is surrounded by 120 feet of fencing, we can set up an equation to represent the perimeter of the garden:

2(l + w) = 120

where l is the length of the garden and w is the width of the garden. We are given that one side length of the garden is 50 feet, so we can substitute this value into the equation:

2(50 + w) = 120

Simplifying the equation, we get:

100 + 2w = 120

Subtracting 100 from both sides of the equation, we get:

2w = 20

Dividing both sides of the equation by 2, we get:

w = 10

So, the width of Garden B is 10 feet. Now, we can calculate the area of Garden B:

Area = l × w = 50 × 10 = 500 square feet

Comparing the Areas of the Two Gardens

Now that we have calculated the areas of both gardens, we can compare the results. Garden A has an area of 875 square feet, while Garden B has an area of 500 square feet. Therefore, Garden A has the largest area.

Conclusion

In this article, we compared the areas of two rectangular gardens, Garden A and Garden B, to determine which one has the largest area. We used the given information to calculate the area of each garden and compared the results. The results show that Garden A has the largest area, with an area of 875 square feet, while Garden B has an area of 500 square feet.

Mathematical Formulas Used

Perimeter of a rectangle: 2(l + w)
Area of a rectangle: l × w

References

[1] "Perimeter and Area of a Rectangle". Math Open Reference. Retrieved 2023-02-20.
[2] "Rectangle". Math Is Fun. Retrieved 2023-02-20.

Glossary

Perimeter: The distance around a shape.
Area: The amount of space inside a shape.
Rectangle: A four-sided shape with opposite sides of equal length.
Length: A measure of how long something is.
Width: A measure of how wide something is.
Frequently Asked Questions (FAQs) About Comparing the Areas of Two Rectangular Gardens =====================================================================================

Q: What is the main difference between Garden A and Garden B?

A: The main difference between Garden A and Garden B is the length of their sides. Garden A has one side length of 25 feet, while Garden B has one side length of 50 feet.

Q: How do you calculate the area of a rectangle?

A: To calculate the area of a rectangle, you need to multiply the length and width of the rectangle. The formula for the area of a rectangle is:

Area = l × w

where l is the length of the rectangle and w is the width of the rectangle.

Q: How do you find the length of the other side of a rectangle when you know the perimeter and one side length?

A: To find the length of the other side of a rectangle when you know the perimeter and one side length, you can use the formula:

2(l + w) = perimeter

where l is the length of the rectangle and w is the width of the rectangle. You can then substitute the value of the perimeter and one side length into the equation and solve for the other side length.

Q: Why is it important to compare the areas of two rectangles?

A: It is important to compare the areas of two rectangles because it can help you determine which rectangle has the largest area. This can be useful in a variety of situations, such as when designing a garden or a building.

Q: What is the formula for the perimeter of a rectangle?

A: The formula for the perimeter of a rectangle is:

Perimeter = 2(l + w)

where l is the length of the rectangle and w is the width of the rectangle.

Q: How do you calculate the width of a rectangle when you know the perimeter and one side length?

A: To calculate the width of a rectangle when you know the perimeter and one side length, you can use the formula:

2(l + w) = perimeter

where l is the length of the rectangle and w is the width of the rectangle. You can then substitute the value of the perimeter and one side length into the equation and solve for the width.

Q: What is the difference between the area of Garden A and the area of Garden B?

A: The area of Garden A is 875 square feet, while the area of Garden B is 500 square feet. Therefore, the area of Garden A is 375 square feet larger than the area of Garden B.

Q: Why is it important to use the correct formula when calculating the area of a rectangle?

A: It is important to use the correct formula when calculating the area of a rectangle because using the wrong formula can result in an incorrect answer. In this case, using the correct formula (Area = l × w) resulted in the correct answer (875 square feet for Garden A and 500 square feet for Garden B).

Q: Can you give an example of a real-world situation where comparing the areas of two rectangles is useful?

A: Yes, an example of a real-world situation where comparing the areas of two rectangles is useful is when designing a garden. For example, you may want to compare the areas of two different garden designs to determine which one will provide the most space for plants.

Q: What is the relationship between the perimeter and the area of a rectangle?

A: The perimeter and the area of a rectangle are related in that the perimeter is the distance around the rectangle, while the area is the amount of space inside the rectangle.