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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?


  1. (BDDC)2

  2. (ABBC)2

  3. (ABAC)2

  4. (ADBD)2


Solution

The correct option is C

(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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