Question

triangle C D E is similar to triangle Q R S and has a ratio of similarity of 4:1. If side RS measures 8 inches, how long is side DE?

Answer 1

Answer:

Side DE = 32 inches

Explanation:

We are given that ΔCDE is similar to ΔQRS, this means that the corresponding sides are equal.

We are also given that the similarity ratio is $\frac{4}{1}$

Now, we set the similarity ratio and equate it to $\frac{4}{1}$ as follows:

$\frac{CD}{QR} = \frac{DE}{RS} = \frac{CE}{QS} = \frac{4}{1}$

We are given that side RS = 8 inches. Substitute with this value in the above ratio and solve for DE as follows:

$\frac{DE}{RS} = \frac{DE}{8} = \frac{4}{1}$

DE = $\frac{4*8}{1} = 32$ inches

Hope this helps :)