Question

11 in triangle △abc, ab = 8 cm, bc = 10 cm, and ac = 12 cm. in triangle △def, de = 16 cm and ef = 20 cm. what is the length of df if △abc ~ △def? a 23 cm b 24 cm c 22 cm d 25 cm

Explanation:

Step1: Find the similarity ratio

Since $\triangle ABC\sim\triangle DEF$, the ratio of corresponding - sides is the same. $\frac{AB}{DE}=\frac{8}{16}=\frac{1}{2}$, $\frac{BC}{EF}=\frac{10}{20}=\frac{1}{2}$.

Step2: Calculate the length of $DF$

Let $DF = x$. We know that $\frac{AC}{DF}=\frac{1}{2}$ (because of the similarity ratio). Given $AC = 12$ cm, then $\frac{12}{x}=\frac{1}{2}$. Cross - multiply gives $x=24$ cm.

Answer:

b. 24 cm