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Question

In a right ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does not give the ratio of the areas of ABD and ACB?


A

(ABAC)2

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B

(ADAB)2

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C

(BDCB)2

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D

(ABAD)2

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Solution

The correct option is D

(ABAD)2


Consider ΔABD and ΔACB:

∠BAD = ∠BAC [common angle]

∠BDA = ∠ABC [ 90]

By AA similarity criterion,
ABD ~ ACB

Hence,

ar(ΔABD)ar(ΔACB)=(ABAC)2=(ADAB)2=(BDCB)2


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