Question

1 figure 1 and figure 2 are similar and have the measurements shown in units figure 1 figure 2 based on the figures, which proportion is true? \\(\frac{x}{y}=\frac{8}{5}\\) \\(\frac{x}{y}=\frac{2}{4}\\) \\(\frac{x}{y}=\frac{4}{2}\\) \\(\frac{x}{y}=\frac{5}{3}\\)

Explanation:

Step1: Find the scale factor

For similar figures, corresponding sides are proportional. First, find the scale factor using the corresponding vertical sides. In Figure 1, the vertical side is 2, and in Figure 2, it's 1.2? Wait, no, wait. Wait, Figure 1 has a vertical side of 2, Figure 2 has 1.2? Wait, no, looking at the horizontal bases: Figure 1 has a base of 5, Figure 2 has a base of 3. Or the top bases: Figure 1 top is 4, Figure 2 top is 2.4? Wait, no, let's check the corresponding sides. The vertical side in Figure 1 is 2, in Figure 2 is 1.2? Wait, no, maybe the vertical sides: Figure 1 has height 2, Figure 2 has height 1.2? Wait, no, the right angles: Figure 1 has height 2, Figure 2 has height 1.2? Wait, no, let's check the ratio of corresponding sides. Let's take the horizontal bases: Figure 1 has a lower base of 5, Figure 2 has lower base of 3. The ratio of 5/3. Now, the side x in Figure 1 and y in Figure 2: x is the slant side in Figure 1, y in Figure 2. Also, the vertical side in Figure 1 is 2, in Figure 2 is 1.2? Wait, no, 2 and 1.2: 2/1.2 = 5/3. Ah, yes! 2 divided by 1.2: 2/1.2 = 10/6 = 5/3. So the scale factor from Figure 1 to Figure 2 is 3/5? Wait, no, Figure 1 to Figure 2: 5 (base) to 3 (base) is 5/3. So corresponding sides should be in ratio 5/3. So x (Figure 1's slant side) to y (Figure 2's slant side) should be 5/3. So x/y = 5/3.

Step2: Verify the proportion

So the proportion x/y = 5/3 is true because the scale factor between the similar figures is 5/3 (since 5 (base of Figure 1) / 3 (base of Figure 2) = 5/3, and 2 (height of Figure 1) / 1.2 (height of Figure 2) = 2/1.2 = 5/3). So the ratio of corresponding sides x and y is 5/3.

Answer:

$\boldsymbol{\frac{x}{y} = \frac{5}{3}}$ (the last option, which is selected in the image)