Understanding the Relationship Between Length and Breadth in a Room Using Ratios

Understanding the relationship between the length and breadth of a room is crucial for various applications in home design, construction, and space optimization. When given the ratio of these dimensions, you can easily determine the actual measurements of the room. In this article, we will walk through the step-by-step process to find the length of a room when the breadth is known and the ratio of the length to breadth is given.

The problem statement is:

The ratio of the length to breadth of a room is 7:5. What is the length of the room if the breadth is 10 meters?

Solving the Problem Using Proportions

To find the length of the room, we can set up a proportion based on the given ratio. Let the length of the room be L and the breadth be B.

Step 1: Setting Up the Proportion

The given ratio is 7:5, which means:

L / B 7 / 5

Given that B is 10 meters:

L / 10 7 / 5

Step 2: Cross Multiplying

Now, we cross-multiply to solve for L:

L * 5 7 * 10

This simplifies to:

5L 70

Step 3: Solving for L

Next, we divide both sides of the equation by 5:

L 70 / 5

This gives us:

L 14 meters

Conclusion

Therefore, the length of the room is 14 meters.

Alternative Methods to Solve the Problem

There are alternative methods to solve this problem, which are equally valid and can be useful for different learners.

Method 1: Using Parts

The ratio 7:5 can be thought of as 7 parts of length corresponding to 5 parts of breadth. If the breadth is 10 meters (5 parts), then each part is 10 / 5 2 meters. Therefore, the length would be 7 parts, i.e., 7 * 2 14 meters.

Method 2: Proportion and Cross-Multiplication

Using the ratio 7:5 as a proportion:

7 / 5 X / 10

Cross-multiplying gives:

5X 7 * 10

Solving for X gives:

X 70 / 5 14 meters

Key Takeaways

This problem demonstrates the practical application of ratios in solving real-world problems. Understanding how to set up and solve proportions based on given ratios is crucial in fields such as architecture, engineering, and interior design. By breaking down the problem into manageable steps and using alternative methods, you can easily find the required measurements and ensure accuracy in your calculations.