Question

In triangle abc if a is 5, b is 12,and c is 13 then length of the median passing through B is
Options
A)
$2 \sqrt{61}$
B)
$\sqrt{61}$
C)
$3 \sqrt{61}$
D)
$4 \sqrt{61}$
​

Answer 1

Given : In triangle ABC  a is 5, b is 12,and c is 13  

To Find  :  length of the median passing through B  

Solution:

a = 5,  b= 12  c= 13

a = BC  , b = AC , c = AB

as 5² + 12² = 13²

Hence triangle is right angle triangle at C

b = 12

Hence median through B  will comes on b = 12

Let say BD is the median

CD = AC/2 = 12/2 = 6

BC = 5

C is right angle

Hence BD² = 5² + 6²

=> BD² = 61

=> BD = √61

Hence median passing through B is √61

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