Question

In triangle ABC,D and E are the points on sides AB and AC respectively such that DE is parallel to BC .If AD=2cm,BD=4cm,show that BC=3DE

Answer 1

Answer:

$ANSWER</p><p></p><p>In △ABC, DE is parallel to BC</p><p></p><p></p><p>Thus, DE divides the two sides AB and AC proportionally.</p><p></p><p></p><p>Thus,</p><p></p><p></p><p>ABAD=ACAE</p><p></p><p></p><p>Thus, △ABC∼△ADE</p><p></p><p></p><p>ADAB=AEAC=DEBC   [C.S.C.T.]</p><p></p><p></p><p>Now,</p><p></p><p></p><p>   AEAC=DEBC</p><p></p><p></p><p>⇒DE=ACAE×BC</p><p></p><p></p><p>⇒DE=52×10  [ ∵AC=(AE+EC)=2+3=5]</p><p></p><p></p><p>⇒DE=4 cm</p><p></p><p>$

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