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Question

In ΔABC, ACB=90, AB = C units, BC = a units, AC = b units, CD is perpendicular to AB and CD = p units. Then 1p2=


  1. Scalene

  2. Isosceles but not right angled

  3. Equilateral

  4. Right Ðd & isosceles


Solution

The correct option is C

Equilateral


ACB=90

AB2=AC2+BC2

c2=b2+a2     ....... (1)

Area (ΔABC)=12×AB×CD

=12×BC×AC

=12×c×p=12×a×b

C=abp

Put this in (1), we get 

a2b2p2=b2+a2

1p2=b2+a2a2b2

1p2=b2a2b2+a2a2b2

1p2=1a2+1b2

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