Question

in the triangle abc~triangle ade.if ad:db=2:3 and de=5cm.1) fnd bc.2) if x be the length of the perpendicular from a to be , find the length of the perpendicular from a to bc in terms of x

Answer 1

Given :  ΔADE ≈ ΔABC   . ad:db=2:3 and de=5cm.   x be the length of the perpendicular from a to de

To find : BC &  length of the perpendicular from a to bc in terms of x

Solution:

ΔADE ≈ ΔABC

=> AD/AB =  DE/BC

=> AD/(AD + DB)  = DE/BC

=> 2/(2 + 3)  = 5/BC

=> BC = 25/2

=> BC = 12.5 cm

as ΔADE ≈ ΔABC

=> Their corresponding altitude will be in the same ratio as sides

hence

AD/AB  = length of the perpendicular from a to de/length of the perpendicular from a to bc

=> 2/5 =  x/length of the perpendicular from a to bc

=> length of the perpendicular from a to bc = 5x/2

BC = 12.5 cm

length of the perpendicular from a to bc = 5x/2

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Answer 2

Step-by-step explanation:

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