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Q.

In a triangle ABC, a = 7, b = 8, c = 9, BD is the median and BE the altitude from the vertex B, then

 COLUMN-I COLUMN-II
A)BDp)2
B)BEq)7
C)EDr)45
D)AEs)6

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a

A−r;B−s;C−q;D−p

b

A−q;B−r;C−p;D−s

c

A−s;B−r;C−q;D−p

d

A−r;B−p;C−q;D−s

answer is C.

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Detailed Solution

detailed_solution_thumbnail

 ΔABD cosA=42+92−BD22×4×9
 = 82+92−722×8×7  (From  ΔABC ) \
⇒BD2=49⇒BD=7⇒ΔBCD  is isosceles
  ⇒ ED= 1/2 CD=2
 And BE =  72−22=45,AE=6
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