Question

n the diagram below, the pentagons are similar. If side BC = 3, Side GH = 21, and side HI = 49, what is the length of side CD?

Answer 1

When two figures are similar, the ratio between corresponding parts of the shapes is the same.

In this case, the segment BC corresponds to GH and the side HI corresponds to CD. Then:

`(CD)/(HI)=(BC)/(GH)`

Replace HI=49, BC=3 and GH=21. Then, solve for CD:

`\begin{gathered} \Rightarrow CD=(BC)/(GH)* HI \\ \\ =(3)/(21)*49 \\ \\ =7 \end{gathered}`

Therefore, the lengh of side CD is 7. The correct choice is option d) 7.