Questions: If triangle ABC is similar to triangle DEF and the scale factor from triangle ABC to triangle DEF is 2, what are the lengths of DE, EF^2, and CF, respectively? A. 8,16,24 B. 4,3,12 C. 1,2,3 D. 2,8,12

If triangle ABC is similar to triangle DEF and the scale factor from triangle ABC to triangle DEF is 2, what are the lengths of DE, EF^2, and CF, respectively?
A. 8,16,24
B. 4,3,12
C. 1,2,3
D. 2,8,12

Transcript text: If $\triangle A B C \sim \triangle D E F$ and the scale factor from $\triangle A B C t o \angle D E F$ is 2 what are the lengths of $\overline{D E}$. $\mathrm{EF}^{2}$, and $\overline{C F}$, respectively? A. $8,16,24$ B. 4,3,12 C. $1,2,3$ D. $2,8,12$

Solution

Solution Steps

Step 1: Find the length of DE

The side lengths of ΔABC are AB = 4, BC = 2, and AC = 1. The scale factor from ΔABC to ΔDEF is 2. Therefore, DE = 2 * AB = 2 * 4 = 8.

Step 2: Find the length of EF

EF corresponds to BC, so EF = 2 * BC = 2 * 2 = 4.

Step 3: Find the length of DF

DF corresponds to AC, so DF = 2 * AC = 2 * 1 = 2.

Final Answer: The lengths of DE, EF, and DF are 8, 4, and 2 respectively. So the answer is D. 2,8,12 (the order of the side lengths was incorrect in the original question.)

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