Question

If the sides of a triangle are 5,6,10, then the length of the median of biggest side is
a) 13/2
b) 11/2
c) 17/2
d) 19/2​

Answer 1

Answer:

answer is (A)

We know, as per Apollonius theorem where a,b and c are the length of sides of a triangle

The length of median M

a

=

2

1

2b

2

+2c

2

−a

2

And M

b

=

2

1

2a

2

+2c

2

−b

2

And M

c

=

2

1

2a

2

+2b

2

−c

2

Given that a=5,b=6 and c=10

Then length of median of the longest side =M

10

=

2

1

2(5)

2

+2(6)

2

−(10)

2

=

2

1

2×25+2×36−100

=

2

1

50+72−100

=

2

1

22

=

2

4.70

=2.35

∴m=2.35

Hence, 100m=235