Question

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.

Answer 1

CD=20 cm and DE=15 cm. CD=20 cm and DE=15 cm.

Explanation:

A rhombus DMFN is inscribed in such a way that it is inscribed in triangle CDE with the vertices M, F, and N l on the sides CD , CE , and DE respectively.

Now, in rhombus, the parallel sides are always parallel, therefore

MF║DE, thus,
`(CM)/(MD)=(CF)/(EF)` by the basic proportionality condition.

It is given that CF=8 cm and EF=12 cm, therefore,
`(CM)/(MD)=(8)/(12)`.

That is CM=8 cm and MD=12 cm. Therefore, CD=CM+MD=8+12=20.

According to question, Perimeter of △CDE =55 cm

⇒CD+DE+CE=55

⇒20+DE+20=55

⇒DE=15 cm

Hence, CD=20 cm and DE=15 cm.

Answer 2

CD=14

DE=21

Explanation: