Understanding Proportions in Building Dimensions: A Math Problem Solved
Mathematics plays a crucial role in various real-world applications, from designing buildings to engineering structures. One common problem involves using ratios to find unknown measurements. In this article, we explore a practical example where the ratio of the length to the width of a building is given, and we need to find the width when the length is known. We'll solve this through a step-by-step approach, ensuring clarity and understanding.
Problem Statement
The problem we aim to solve is: If the ratio of the length to the width of a building is 4:3, and the length is 48 units, what is the width?
Solution
Let's denote the width of the building as w.
We are given that the ratio of the length to the width (length : width) is 4:3. This can be written as:
[ frac{text{Length}}{text{Width}} frac{4}{3} ]Substituting the given length of 48 units into the equation:
[ frac{48}{text{w}} frac{4}{3} ]To solve for w, we cross-multiply:
[ 48 cdot 3 4 cdot text{w} ]Performing the multiplication on the left side:
[ 144 4 cdot text{w} ]Next, we divide both sides of the equation by 4 to isolate w:
[ text{w} frac{144}{4} 36 ]Hence, the width of the building is 36 units.
Verification
To ensure our solution is correct, we can check if the ratio of the length to the width is indeed 4:3:
[ frac{48}{36} frac{4}{3} ]This verifies that the ratio is correct, confirming our calculation.
Conclusion
Mathematics, particularly the use of proportions, is a powerful tool in solving real-world problems. In this case, solving the problem of finding the width of a building when the length and the ratio are known, we used the fundamental principles of proportions to reach a clear and accurate solution.