Question 1132732
here is a picture to use as reference

<a href="http://tinypic.com?ref=33p7d06" target="_blank"><img src="http://i66.tinypic.com/33p7d06.jpg" border="0" alt="Image and video hosting by TinyPic"></a>

draw same picture and mark points as given


A rhombus {{{DMFN}}} is inscribed in this triangle so that vertices {{{M}}}, {{{F}}}, and {{{N }}}lie on the sides {{{CD}}} , {{{CE}}} , and {{{DE}}} respectively.


Since, in rhombus, the opposite edges are parallel,

{{{MF}}} ║ {{{DE}}} 

=>{{{CM/MD=CF/EF }}}

since given that {{{CF=8cm}}} and {{{EF=12cm }}}, we have

=>{{{ CM/MD=8/12}}}

That is, {{{CM=8}}} and {{{MD= 12}}}

Therefore, {{{CD=CM+MD=8+12=20}}}

But According to the question, 

{{{CD+DE+CE=55}}}

=>{{{20+DE+20=55}}}

=> {{{DE=15}}}


Answer:  {{{CD= 20cm }}}and {{{DE= 15cm}}}