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

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

: )

answer: an 8-foot rope is tied from the top of a pole to a

stake in the ground, as shown in the diagram

below

step-by-step explanation: