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Question

In a right angled 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

Since, in BDC, DBC=90C=A and in ABC,A=90C,
BAD=DBC  
and BDA=BDC   [90]

By AA similarity criterion, ADBBDC

Hence,
Ar(ΔABD)Ar(ΔBDC)=(ABBC)2=(ADBD)2=(BDDC)2

Thus, the option (ABAC)2 is required answer.


Mathematics

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