Question

In the given figure, ΔABC ~ ΔADE. If AE : EC = 4 : 7 and DE = 6.6 cm, find BC. If ‘x’ be the length of the perpendicular from A to DE, find the length of perpendicular from A to BC in terms of ‘x’. 

Answer 1

ΔABC ∼ ΔADE

AE : EC = 4 : 7, DE = 6.6 cm, BC = ?

Draw AL ⊥ DE and AM ⊥ BC

And AL = x cm

Find AM in terms of x

∵ ΔADE ∼ ΔABC

∴ `(AE)/(AC) = (DE)/(BC)`

∴ `(AE)/(AC) = (AE)/(AE + EC) = 4/(4 + 7) = 4/11`

∴ `(DE)/(BC) = (AE)/(AC) \implies 4/11 = 6.6/(BC)`

`\implies BC = (6.6 xx 11)/4`

= `36.3/2`

= 18.15 cm

∵ AL ⊥ DE and on producing it to BC then AM ⊥ BC

`(AL)/(AM) = (AE)/(AC) \implies x/(AM) = 4/11`

`\implies AM = (11 xx x)/4 = 11/4 x`