Question

d. grid with two squares e. rectangle with height 1, length 6; rectangle with height 2.5, length 15

Explanation:

Since the problem isn't clearly stated (e.g., what to find about the figures: area, scale factor, etc.), I'll assume we might be looking at similar rectangles in part (e) and checking if they are similar or finding a scale factor. Let's assume we need to check if the rectangles are similar.

For part (e):

Step 1: Identify dimensions of first rectangle

First rectangle: length \( l_1 = 6 \), height \( h_1 = 1 \)

Step 2: Identify dimensions of second rectangle

Second rectangle: length \( l_2 = 15 \), height \( h_2 = 2.5 \)

Step 3: Check ratio of lengths and heights

Ratio of lengths: \( \frac{l_2}{l_1} = \frac{15}{6} = 2.5 \)
Ratio of heights: \( \frac{h_2}{h_1} = \frac{2.5}{1} = 2.5 \)
Since both ratios are equal, the rectangles are similar with a scale factor of 2.5.

If the question was about area, for the first rectangle area \( A_1 = 6 \times 1 = 6 \), second \( A_2 = 15 \times 2.5 = 37.5 \), and \( \frac{A_2}{A_1} = \frac{37.5}{6} = 6.25 = (2.5)^2 \), which matches the square of the scale factor.

For part (d), if we assume each grid square has side length 1:

• Small square: let's say side length \( s_1 = 3 \) (counting grid squares), area \( A_1 = 3^2 = 9 \)
• Large square: side length \( s_2 = 5 \) (counting grid squares), area \( A_2 = 5^2 = 25 \)

If checking similarity, ratio of sides \( \frac{5}{3} \), ratio of areas \( \frac{25}{9} = (\frac{5}{3})^2 \), so they are similar squares (all squares are similar) with scale factor \( \frac{5}{3} \approx 1.666... \)

Since the problem details are missing, but based on common Eureka Math problems, likely about similar figures (scale factor, area ratio). If we take part (e) and find the scale factor:

Step1: Find length ratio

\( \frac{15}{6} = 2.5 \)

Step2: Find height ratio

\( \frac{2.5}{1} = 2.5 \)

Step3: Conclude scale factor

Since ratios are equal, scale factor is 2.5.

Answer:

The scale factor (if checking similarity) is \( 2.5 \) (or \( \frac{5}{2} \)). If area, first area \( 6 \), second \( 37.5 \), ratio \( 6.25 \).

(Note: Since the original problem's question is not specified, this is a common interpretation. If the actual question is different, please clarify.)