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 ,
2 answers:
Answer:
CD=20 cm and DE=15 cm. CD=20 cm and DE=15 cm.
Step-by-step 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, by the basic proportionality condition.
It is given that CF=8 cm and EF=12 cm, therefore, .
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.
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