Since the rectangles are similar, their corresponding side lengths are proportional. We can set up a proportion between the side lengths of the two rectangles to find the missing side.

Let $x$ represent the missing side length of the first rectangle.

Given:

• Width of the first rectangle = 10
• Unknown height of the first rectangle = $x$
• Width of the second rectangle = 15
• Height of the second rectangle = 24

Proportion Setup

Since the rectangles are similar: $\frac{10}{15} = \frac{x}{24}$

Solving for $x$:

1. Cross-multiply to eliminate the fraction: $10 \cdot 24 = 15 \cdot x$
2. Simplify: $240 = 15x$
3. Divide by 15: $x = \frac{240}{15} = 16$

Answer

The missing side length is $\mathbf{16}$.

Would you like further explanation, or do you have any questions?

Here are five related questions:

1. What would the missing side be if the larger rectangle had a height of 30 instead?
2. How do we determine if two shapes are similar?
3. What happens to the ratio of the areas of similar rectangles?
4. How would you find the perimeter of the smaller rectangle with this missing length?
5. Can we use this method for other shapes, like triangles or circles?

Tip: For similar figures, the ratios of corresponding sides are always equal.