Question

Consider the glven solids with the dimensions shown. Which solids are similar?

Answer 1

Answer: Choice A) only figure 1 and figure 2

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Explanation:

Let's assume that figure 2 is similar to figure 3.

If this is the case, then the horizontal portions would divide to 30/15 = 2, showing that figure 3 has sides that are twice as long compared to figure 2. But then notice that the vertical sides divide to 36/24 = 1.5, which doesn't match with the previous result of 2.

Figures 2 and 3 cannot be similar for that reason.

Also, figures 1 and 3 are not similar either. Note the horizontal portions divide to 30/10 = 3 while the vertical portions divide to 36/16 = 2.25; the results 3 and 2.25 don't match.

We eliminate answers B, C and D. The only thing left is choice A.

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To verify choice A is true, we divide each corresponding piece like so

• Horizontal: 15/10 = 1.5
• Vertical: 24/16 = 1.5
• Slanted: 12/8 = 1.5

Each division leads to the same result of 1.5, meaning that figure 2's side lengths are 1.5 times longer than the corresponding side lengths of figure 1. So this confirms that figure 1 is similar to figure 2.

Answer 2

Answer:

A) only figure 1 and figure 2

Step-by-step explanation: