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Question

In Δ ABC, D is a point on side BC.  Find AB, if AC=3 cm, AD=3cm, BD=8cm and CD=1cm.
  1. 6 cm
  2. 7 cm
  3. 9 cm
  4. 11 cm


Solution

The correct option is C 9 cm

Drop a perpendicular from A on DC at E. Now,

ΔAEDΔ AEC by RHS congruency,
so that, DE=EC=(12)DC=0.5 cm
also

ar(ΔADC)=(12)×DC×AE=(s×(sa)×(sb)×(sc))2 where, s is the semi-perimeter of the triangle
or, AE2=(4×(3.5)×(0.5)×(0.5)×(2.5)1)cm2=8.75 cm2
Now in right ΔAEB,AB2=EB2+AE2=(ED+DB)2+AE2=(8.5)2+8.75 = 81 cm2,
therefore, AB = 9 cm

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