Understanding the Ratio of Rectangle Dimensions: Calculating Length from Width

In this article, we will explore the concept of the ratio of the length to width of a rectangle and how to find the length when the width is given. Specifically, we will examine a rectangle where the ratio of the length to the width is 4:3 and the width is known to be 36 cm. We will walk through two different methods to solve this problem.

Method 1: Direct Proportional Calculation

Given that the ratio of the length to the width of the rectangle is 4:3, and the width is 36 cm, we can set up a proportion to find the length.

Proportion: Length/width 4/3

Substituting the given width (36 cm) into the equation:

Proportion: Length (4/3) × 36 cm

To simplify the calculation, we can first multiply the numerator by 36:

4 × 36 144

Now, divide by the denominator (3):

144 ÷ 3 48

Therefore, the length of the rectangle is 48 cm.

Method 2: Using a Common Factor

Another way to approach this problem is by using a common factor. Let's denote the common factor as x. This means that the length (which is four times the common factor) and the width (which is three times the common factor) can be represented as 4x and 3x respectively.

Given that the width is 36 cm, we set up the equation:

Equation: 3x 36 cm

Solving for x, divide both sides by 3:

x 36 ÷ 3 12

Now that we have found the common factor (x 12), we can find the length:

Equation: 4x 4 × 12 cm 48 cm

Again, we find that the length of the rectangle is 48 cm.

Conclusion

In both methods, we arrived at the same conclusion that the length of the rectangle is 48 cm. This problem demonstrates the usefulness of ratios in solving geometric problems and provides a clear methodology for students and professionals in geometry, engineering, and design.

Keywords: rectangle dimensions, ratio calculation, geometric properties