Question

In figure triangle abc and ebs are on the same base bc. if ae produced intersect bc at d then prove that ar(abc)/ar(ebc)=ad/ed

Answer 1

See the diagram.

Draw perpendiculars AF and EG from A and E respectively onto BCD.

Area(ΔABC) = 1/2 * BC * AF 
Area(ΔEBC) = 1/2 * BC * EG

Hence their ratio = AF / EG  --- (1)

ΔAFD and ΔEGD are similar as  AF || EG, AD || ED and FD || GD.
So  the ratio    AF / EG = AD / ED

Hence  by (1), Area(ΔABC) / Area(ΔEBC) = AD / ED