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

Side DE = 32 inches

Step-by-step 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
`(4)/(1)`

Now, we set the similarity ratio and equate it to
`(4)/(1)` as follows:

`(CD)/(QR) = (DE)/(RS) = (CE)/(QS) = (4)/(1)`

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

`(DE)/(RS) = (DE)/(8) = (4)/(1)`

DE =
`(4*8)/(1) = 32` inches

Hope this helps :)