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 (AABD):ar (ABDC) =
[]
(B) 16:9 (C) 9 : 25
(D) 16:25
(A)9:16
Answers
I think it's option a)
. .
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)
(A)9:16
(B) 16:9
(C) 9 : 25
(D) 16:25
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
option A) is correct
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