The perimeter of △cde is 55 cm. a rhombus dmfn is inscribed in this triangle so that vertices m, f, and n lie on the sides cd, ce, and de respectively. find cd and de if cf=8 cm and ef=12 cm.

CD=14

DE=21

Step-by-step explanation:

ΔCDE is similar to ΔFNE (∠E≅∠E, ∠NFE≅∠DCE) by AA similarity

Using Thales' Intercept Theorem Corollary, you know that:

EN/ED=EF/EC=NF/CD=12/20

Let DN be 8x and NE be 12x

Let NF be 12y and CD be 20y

Then you have a system of equations:

20x+20y+20=55

8x=12y

By solving them, you get y=0.7 and x=1.05⇒

DE=21 and CD=14

it is probably the graph on the bottom right.