In a right triangle $Δ$ ABC with right angle at B, BD is a perpendicular, dropped onto the hypotenuse. If AC = 2AB, what is the area of $Δ$ ABD, given, area of $Δ$ ABC = 5 sq units.

0.5 sq. unit

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1 sq. unit

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1.25 sq. unit

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5 sq. unit

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Solution

The correct option is C
1.25 sq. unit

$G i v e n, \frac{A B}{A C} = \frac{1}{2} a n d A r (Δ A B C) = 5 s q . u n i t s C o n s i d e r Δ A B D a n d Δ A B C : ∠ B A D = ∠ B A C - - - - [c o m m o m a n g l e] ∠ B D A = ∠ A B C - - - - [90^{\circ}] By AA similarity criterion, Δ A B D \sim Δ A B C H e n c e, \frac{A r (Δ A B D)}{A r (Δ A B C)} = {(\frac{A B}{A C})}^{2} = {(\frac{1}{2})}^{2} = \frac{1}{4} i . e ., A r (Δ A B D) \times 4 = A r (Δ A C B) \Rightarrow A r (Δ A B D) = \frac{5}{4} = 1.25 s q . u n i t s H e n c e t h e a r e a o f Δ A B D i s 1.25 s q . u n i t s$

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In a right triangle ΔABC with right angle at B, BD is a perpendicular, dropped onto the hypotenuse. If AC = 2AB, what is the area of Δ ABD, given, area of Δ ABC = 5 sq units.

In a right triangle $Δ$ ABC with right angle at B, BD is a perpendicular, dropped onto the hypotenuse. If AC = 2AB, what is the area of $Δ$ ABD, given, area of $Δ$ ABC = 5 sq units.