Answer :

kvnmurty
We use  Thales theorem of intercepts or from laws of  similar triangles,

We assume that  the line segments D D1,  D1 D2, D2 D3 , D3 D4 and D4 D5 are equal in length.

   D D3 / DA  =  D D5 / DE
   D D5 / D D3  =  DE / DA
     5 / 3  = DE / DA     =>     DE = 5 cm * 5 /3 = 25 / 3  cm

DAB and DBE are similar triangles  as the similar sides are parallel.
   Hence the triangle DBE is also equilateral triangle of side  25/3 cm.

garimakataria1610

STEP BY STEP EXPLANATION :

We use  Thales theorem of intercepts or from laws of  similar triangles,

We assume that  the line segments D D1,  D1 D2, D2 D3 , D3 D4 and D4 D5 are equal in length.

D D3 / DA  =  D D5 / DE

D D5 / D D3  =  DE / DA

5 / 3  = DE / DA     =>     DE = 5 cm * 5 /3 = 25 / 3  cm

DAB and DBE are similar triangles  as the similar sides are parallel.

Hence the triangle DBE is also equilateral triangle of side  25/3 cm.

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