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Answer 1 · 2016-07-15T09:07:28

$C E = 5.6$ $CE=5.6$ cm, and, $B C = 3.2$ $BC=3.2$ cm.

Observe that line $A B ∣ ∣ D E, &, B D$ $AB || DE, &, BD$ is a transverse.

$:. m/_ABC=m/_ABD=m/_BDE=m/_CDE$ .........[Alternate Angles]

Also, $m/_ACB=m/_ECD$ ...........[Opposite Angles].

Thus, $DeltaABC ~~ DeltaEDC$ , by the correspondence,
$ABC harr EDC$

Since the corresponding sides of similar $Delta$ are proportionate, we have,

$(AB)/(ED)=(BC)/(DC)=(CA)/(CE) rArr 4/8=(BC)/6.4=2.8/(CE)$

$rArr BC=3.2, &, CE=5.6$