Question

drag the similar figure into the table. original figure: blue rectangle with top and bottom length 2, side length 5 similar figure: area to drag and drop figures to choose from: blue rectangle with top and bottom length 4, side length 10, red rectangle with top and bottom length 3, side length 6, orange square with top and bottom length 6, side length 6

Explanation:

Step1: Find scale factor

Original figure: width = 2, height = 5. Check ratios of other figures.

• Blue: width=4, height=10. Ratio: $\frac{4}{2}=2$, $\frac{10}{5}=2$ (scale up, not similar in size here? Wait, no—wait, the problem says "similar figure" (maybe similar in shape, and we need the one with same aspect ratio). Wait, original aspect ratio: $\frac{width}{height}=\frac{2}{5}=0.4$.
• Red: width=3, height=6. Ratio: $\frac{3}{6}=0.5$ (no). Wait, wait, maybe I mixed width/height. Original: height 5, width 2. So height/width = 5/2 = 2.5.
• Blue: height 10, width 4. 10/4 = 2.5 (same ratio). But wait, the problem says "similar figure"—maybe the red one? Wait no, wait the original is a rectangle with width 2, height 5. Let's check the red figure: width 3, height 6. 6/3 = 2 (not 2.5). Wait, blue: 10/4 = 2.5 (same as 5/2). Wait, but the problem says "similar figure"—maybe the one with the same shape (same aspect ratio) and maybe same proportions. Wait, original: width 2, height 5. Let's check the ratios of each figure:

Original: width = 2, height = 5. Aspect ratio (height/width) = 5/2 = 2.5.

Blue figure: width=4, height=10. 10/4 = 2.5 (same aspect ratio, but scaled up).

Red figure: width=3, height=6. 6/3 = 2 (different).

Orange figure: width=6, height=6. 6/6 = 1 (different).

Wait, maybe the problem is about similar figures (same shape, so same aspect ratio) and we need the one that's similar (same aspect ratio). Wait, original aspect ratio: 2/5 (width/height) or 5/2 (height/width). Let's check each:

• Blue: 4/10 = 2/5 (same as original width/height). So aspect ratio matches. But wait, the original is smaller. Wait, maybe I misread—maybe the "similar figure" is the one with the same aspect ratio. Wait, the original is width 2, height 5. Let's check the red: 3/6 = 1/2 (no). Blue: 4/10 = 2/5 (yes). Wait, but the problem says "similar figure"—maybe the one that's a scaled version. Wait, but the original is 2x5, blue is 4x10 (scale factor 2), red is 3x6 (scale factor 1.5), orange is 6x6 (square). Wait, maybe the question is to find the similar figure (same shape, so same aspect ratio). So blue has same aspect ratio (2/5 = 4/10), red is 3/6=1/2, orange is 1. So blue has same aspect ratio. But wait, maybe the problem is about "similar" in shape and size (congruent? No, similar). Wait, maybe I made a mistake. Wait, original figure: width 2, height 5. Let's check the ratios of width and height for each candidate:

1. Blue (top): width 4, height 10. 4/2 = 2, 10/5 = 2. So scale factor 2 (enlargement). But the problem says "similar figure"—maybe that's the one. Wait, but the other figures: red (middle) width 3, height 6. 3/2 = 1.5, 6/5 = 1.2 (not same scale). Orange: 6/2=3, 6/5=1.2 (no). So blue has same scale factor (2), so same shape (similar). So the blue figure (width 4, height 10) is similar. Wait, but the problem says "drag the similar figure into the table"—maybe that's the one. Wait, but let's confirm the aspect ratio. Original: 2/5 = 0.4. Blue: 4/10 = 0.4. Red: 3/6 = 0.5. Orange: 6/6 = 1. So blue has same aspect ratio. So the blue figure (top one, width 4, height 10) is similar.

Step2: Confirm similarity

Similar figures have proportional corresponding sides. So since 4/2 = 10/5 = 2, the blue figure is similar (scaled by 2). The other figures don't have proportional sides (red: 3/2 ≠ 6/5; orange: 6/2 ≠ 6/5). So the blue figure (width 4, height 10) is the similar one.

Answer:

The blue figure (top one with width 4 and height 10)