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Question

In a right angle triangle ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of ABD and BCD?


A

(ABBC)2

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B

(ABAC)2

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C

(ADBD)2

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D

(BDDC)2

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Solution

The correct option is B

(ABAC)2



Consider ABD and BCD:
BAD=DBC [Since, in BDC, DBC=90C=A and in ABC, A=90C]
BDA=BDC [90]
By AA similarity criterion, ADBBDC
Hence,

Ar(ABD)Ar(BDC)=(ABBC)2=(ADBD)2=(BDDC)2

Option B is the odd one out among these options as can be seen from the above equation.


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