Finding the Dimensions of the Store

Oct 13, 2025 by talynt.org 22 views

Introduction

Mathematics is an essential tool for solving real-world problems. In this article, we will use mathematical concepts to find the dimensions of a rectangular store. The store has an area of 2,700 square feet, and we need to find its length and width. We will use a table to represent the given information and then apply mathematical operations to find the solution.

Given Information

	Length (L)	Width (W)	Area (A)
A	6	3	18
B	7	8	56
C	9	5	45
D	9	9	90

Understanding the Problem

The problem states that the store is rectangular in shape and has an area of 2,700 square feet. We need to find the length and width of the store. To do this, we can use the formula for the area of a rectangle, which is A = L × W, where A is the area, L is the length, and W is the width.

Finding the Dimensions of the Store

Let's analyze the given information in the table. We can see that the area of the store is 2,700 square feet, but we don't know the length and width. However, we can use the given information to find the dimensions of the store.

We can start by finding the length and width of each row in the table. For example, in row A, the length is 6 and the width is 3, so the area is 6 × 3 = 18. Similarly, in row B, the length is 7 and the width is 8, so the area is 7 × 8 = 56.

Using Algebraic Equations to Find the Dimensions

Let's use algebraic equations to find the dimensions of the store. We know that the area of the store is 2,700 square feet, so we can set up an equation:

L × W = 2,700

We can also use the given information in the table to set up another equation. For example, in row A, the length is 6 and the width is 3, so we can set up the equation:

6 × 3 = 18

Similarly, in row B, the length is 7 and the width is 8, so we can set up the equation:

7 × 8 = 56

Solving the System of Equations

We can solve the system of equations using substitution or elimination. Let's use substitution. We can solve the first equation for L:

L = 2,700 / W

Substituting this expression for L into the second equation, we get:

(2,700 / W) × W = 56

Simplifying the equation, we get:

2,700 = 56W

Dividing both sides by 56, we get:

W = 2,700 / 56

W = 48.21

Now that we have found the width, we can find the length by substituting the value of W into one of the original equations. Let's use the first equation:

L × 48.21 = 2,700

Dividing both sides by 48.21, we get:

L = 2,700 / 48.21

L = 56.04

Conclusion

In this article, we used mathematical concepts to find the dimensions of a rectangular store. We analyzed the given information in the table and set up algebraic equations to find the length and width of the store. We solved the system of equations using substitution and found the dimensions of the store to be approximately 56.04 feet by 48.21 feet.

Real-World Applications

The problem of finding the dimensions of a rectangular store has many real-world applications. For example, architects and builders need to know the dimensions of a building to design and construct it. Similarly, engineers need to know the dimensions of a machine or a structure to design and build it.

Mathematical Concepts Used

The problem of finding the dimensions of a rectangular store uses several mathematical concepts, including:

Algebraic equations
Substitution
Elimination
Division
Multiplication

These mathematical concepts are essential for solving real-world problems and are used in many fields, including architecture, engineering, and science.

Final Thoughts

Q: What is the formula for finding the area of a rectangle?

A: The formula for finding the area of a rectangle is A = L × W, where A is the area, L is the length, and W is the width.

Q: How do I find the dimensions of a rectangular store if I know the area?

A: To find the dimensions of a rectangular store if you know the area, you can use the formula A = L × W and solve for L and W. You can use algebraic equations and substitution or elimination to find the values of L and W.

Q: What if I have multiple rows of data with different lengths and widths? How do I find the dimensions of the store?

A: If you have multiple rows of data with different lengths and widths, you can use the same formula A = L × W and solve for L and W for each row. Then, you can compare the values of L and W for each row to find the dimensions of the store.

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

A: Yes, you can use a calculator to find the dimensions of the store. Simply enter the values of L and W into the calculator and use the formula A = L × W to find the area. Then, use the inverse operation to find the values of L and W.

Q: What if I have a non-integer value for the area? How do I find the dimensions of the store?

A: If you have a non-integer value for the area, you can use a calculator or a computer program to find the dimensions of the store. Simply enter the value of the area into the calculator or program and use the formula A = L × W to find the values of L and W.

Q: Can I use this method to find the dimensions of any shape?

A: No, this method is only applicable to finding the dimensions of a rectangular shape. If you have a non-rectangular shape, you will need to use a different method to find its dimensions.

Q: What are some real-world applications of finding the dimensions of a rectangular store?

A: Some real-world applications of finding the dimensions of a rectangular store include:

Architecture: Architects use the dimensions of a building to design and construct it.
Engineering: Engineers use the dimensions of a machine or a structure to design and build it.
Interior Design: Interior designers use the dimensions of a room to design and furnish it.
Construction: Construction workers use the dimensions of a building to construct it.

Q: What are some common mistakes to avoid when finding the dimensions of a rectangular store?

A: Some common mistakes to avoid when finding the dimensions of a rectangular store include:

Not using the correct formula for finding the area of a rectangle.
Not solving for L and W correctly.
Not using the correct units of measurement.
Not checking the dimensions of the store for accuracy.

Q: How can I practice finding the dimensions of a rectangular store?

A: You can practice finding the dimensions of a rectangular store by using online calculators or computer programs to solve problems. You can also use real-world examples, such as finding the dimensions of a room or a building, to practice your skills.