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प्रश्न
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'.
उत्तर
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`
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