Question

In a triangle ABC, AB = 6 cm BC = 8 cm and AC = 10 cm from B perpendicular is
drawn on AC to cut AC at D. then ar (triangle ABD): ar (triangle BDC) =​

Answer 1

Answer:

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Answer 2

Given :  In a triangle ABC, AB = 6 cm BC = 8 cm and AC = 10 cm

from B perpendicular is drawn on AC to cut AC at D.

To Find : ar (ΔABD):ar (ΔBDC)

Solution:

AB = 6 cm BC = 8 cm and AC = 10 cm

10² = 8² + 6²

AC² = BC² + AB²

Using converse of Pythagorean theorem , ΔABC is  right angle triangle

right angled at B

ΔABD  and ΔBCD

∠ABD = ∠BCD      = (90° - ∠A)

∠ADB = ∠BDC  = 90°

=>  ΔABD  ~ ΔBCD   ( using AA similarity)

=> AB/BC = BD/CD = AD/BD

=> 6/8 = BD/CD = AD/BD

6/8 = 3/4

Ratio of Area of  Similar triangle = ( ratio of corresponding sides)²

Ar ( ΔABD) / Ar ( ΔBCD)  = ( 3/4)²

=> Ar ( ΔABD) / Ar ( ΔBCD)  = 9/16

=> Ar ( ΔABD) : Ar ( ΔBCD)  = 9 : 16

Ar ( ΔBCD) = Ar (ΔBDC)  as both are same  triangle

Ar ( ΔABD) : Ar ( ΔBDC)  = 9 : 16

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