A Rectangle Has An Area Of 150 M\[$^2\$\]. If One Side Is 25 M, Then How Long Is The Length Of The Adjacent Side?A. 60 M B. 37.5 M C. 6 M D. 0.6 M

Feb 27, 2025 by ADMIN 152 views

A Rectangle's Area and Side Length: Unraveling the Mystery of 150 m^2

Introduction

In the realm of mathematics, particularly geometry, understanding the properties of shapes is crucial for solving various problems. One such problem involves finding the length of an adjacent side of a rectangle when its area and one side length are given. In this article, we will delve into the world of rectangles, explore the relationship between area and side lengths, and provide a step-by-step solution to find the length of the adjacent side.

The Formula for the Area of a Rectangle

The area of a rectangle is given by the formula:

Area = Length × Width

In this problem, we are given the area of the rectangle as 150 m^2 and one side length as 25 m. We need to find the length of the adjacent side, which is the width of the rectangle.

Given Information

Area of the rectangle: 150 m^2
One side length: 25 m

Step 1: Substitute the Given Values into the Formula

We can substitute the given values into the formula for the area of a rectangle:

150 = 25 × Width

Step 2: Solve for the Width

To find the width, we need to isolate the variable "Width" by dividing both sides of the equation by 25:

Width = 150 ÷ 25

Step 3: Calculate the Width

Now, we can calculate the width by performing the division:

Width = 6

Conclusion

Therefore, the length of the adjacent side of the rectangle is 6 m.

Discussion

This problem involves a simple application of the formula for the area of a rectangle. By substituting the given values into the formula and solving for the width, we were able to find the length of the adjacent side. This type of problem is essential in mathematics, as it helps students develop problem-solving skills and understand the properties of shapes.

Real-World Applications

The concept of finding the length of an adjacent side of a rectangle has numerous real-world applications, such as:

Architecture: When designing buildings, architects need to calculate the area of rooms, walls, and other structures to ensure that they are proportional and functional.
Engineering: Engineers use geometric calculations to design and optimize systems, such as bridges, roads, and buildings.
Interior Design: Interior designers use geometric calculations to determine the size and layout of rooms, furniture, and other design elements.

Conclusion

In conclusion, finding the length of an adjacent side of a rectangle is a fundamental concept in mathematics that has numerous real-world applications. By understanding the properties of shapes and applying mathematical formulas, we can solve problems and make informed decisions in various fields.

Frequently Asked Questions

What is the formula for the area of a rectangle? The formula for the area of a rectangle is Area = Length × Width.
How do I find the length of an adjacent side of a rectangle? To find the length of an adjacent side of a rectangle, substitute the given values into the formula for the area of a rectangle and solve for the width.
What are some real-world applications of finding the length of an adjacent side of a rectangle? Some real-world applications of finding the length of an adjacent side of a rectangle include architecture, engineering, and interior design.

References

Geometry: A comprehensive guide to geometry, including the properties of shapes and mathematical formulas.
Mathematics: A textbook on mathematics that covers various topics, including geometry and problem-solving skills.
Online Resources: Websites and online resources that provide tutorials, examples, and practice problems on geometry and problem-solving skills.

Introduction

In our previous article, we explored the concept of finding the length of an adjacent side of a rectangle when its area and one side length are given. We provided a step-by-step solution to find the length of the adjacent side and discussed the real-world applications of this concept. In this article, we will address some frequently asked questions related to this topic.

Q&A

Q1: What is the formula for the area of a rectangle?

A1: The formula for the area of a rectangle is Area = Length × Width.

Q2: How do I find the length of an adjacent side of a rectangle?

A2: To find the length of an adjacent side of a rectangle, substitute the given values into the formula for the area of a rectangle and solve for the width.

Q3: What are some real-world applications of finding the length of an adjacent side of a rectangle?

A3: Some real-world applications of finding the length of an adjacent side of a rectangle include:

Architecture: When designing buildings, architects need to calculate the area of rooms, walls, and other structures to ensure that they are proportional and functional.
Engineering: Engineers use geometric calculations to design and optimize systems, such as bridges, roads, and buildings.
Interior Design: Interior designers use geometric calculations to determine the size and layout of rooms, furniture, and other design elements.

Q4: What if I have a rectangle with an area of 200 m^2 and one side length of 20 m? How do I find the length of the adjacent side?

A4: To find the length of the adjacent side, substitute the given values into the formula for the area of a rectangle and solve for the width:

200 = 20 × Width

Width = 200 ÷ 20

Width = 10

Therefore, the length of the adjacent side of the rectangle is 10 m.

Q5: Can I use this formula to find the length of an adjacent side of a square?

A5: Yes, you can use this formula to find the length of an adjacent side of a square. Since a square is a special type of rectangle with equal side lengths, you can substitute the given values into the formula and solve for the width.

Q6: What if I have a rectangle with an area of 300 m^2 and one side length of 15 m? How do I find the length of the adjacent side?

A6: To find the length of the adjacent side, substitute the given values into the formula for the area of a rectangle and solve for the width:

300 = 15 × Width

Width = 300 ÷ 15

Width = 20

Therefore, the length of the adjacent side of the rectangle is 20 m.

Q7: Can I use this formula to find the length of an adjacent side of a rectangle with a negative area?

A7: No, you cannot use this formula to find the length of an adjacent side of a rectangle with a negative area. The area of a rectangle is always a positive value, so you will get a negative result if you try to use this formula with a negative area.

Q8: What if I have a rectangle with an area of 400 m^2 and one side length of 25 m? How do I find the length of the adjacent side?

A8: To find the length of the adjacent side, substitute the given values into the formula for the area of a rectangle and solve for the width:

400 = 25 × Width

Width = 400 ÷ 25

Width = 16

Therefore, the length of the adjacent side of the rectangle is 16 m.

Conclusion

Frequently Asked Questions

What is the formula for the area of a rectangle? The formula for the area of a rectangle is Area = Length × Width.
How do I find the length of an adjacent side of a rectangle? To find the length of an adjacent side of a rectangle, substitute the given values into the formula for the area of a rectangle and solve for the width.
What are some real-world applications of finding the length of an adjacent side of a rectangle? Some real-world applications of finding the length of an adjacent side of a rectangle include architecture, engineering, and interior design.

References

Geometry: A comprehensive guide to geometry, including the properties of shapes and mathematical formulas.
Mathematics: A textbook on mathematics that covers various topics, including geometry and problem-solving skills.
Online Resources: Websites and online resources that provide tutorials, examples, and practice problems on geometry and problem-solving skills.