A rectangle has a length of 15 cm and a width of 10 cm. A similar rectangle has a length of 45 cm. What is its width? - Aurero
Title: How to Find the Width of a Similar Rectangle Using Scale Ratios
Title: How to Find the Width of a Similar Rectangle Using Scale Ratios
When exploring geometry, one of the most fundamental concepts is similarity between shapes. If two rectangles are similar, their corresponding sides are proportional—meaning the ratio of length to width remains constant across both rectangles.
Let’s analyze a real-life example:
Suppose we have a rectangle with a length of 15 cm and a width of 10 cm. This rectangle has length-to-width ratio:
15 cm ÷ 10 cm = 1.5
Understanding the Context
Now, consider a similar rectangle where the length is 45 cm. Since the rectangles are similar, their ratio must stay the same. To find the new width, we use the same proportion:
Length of larger rectangle / Width of larger rectangle = Length of original / Width of original
45 cm ÷ W = 15 cm ÷ 10 cm
45 cm ÷ W = 1.5
To solve for W (the width), rearrange the equation:
W = 45 cm ÷ 1.5
W = 30 cm
Conclusion:
The width of the similar rectangle with a length of 45 cm is 30 cm. By applying the concept of proportional sides, we efficiently preserved the shape’s similarity while scaling up the dimensions. Remember, in similar rectangles, multiplying the width (or length) by the same scale factor applied to the length maintains proportionality.
Key Insights
Keywords: similar rectangles, rectangle proportions, length and width ratio, geometry scale factor, rectangular similarity, math problem solution, proportional reasoning in geometry
Meta Description:
Learn how to find the width of a similar rectangle using proportions. With a length of 45 cm and original dimensions 15 cm × 10 cm, this guide shows how scaling preserves shape while calculating the new width accurately.
