Solve question 80 ?
2 Answers
Answer is "half the". While perimeter of a triangle is greater than sum of its medians, sum of its medians is greater than half the perimeter.
Explanation:
Let us consider
Now it is easy to prove that
Now consider
or
Similarly we have
Adding the three, we get
or
However, also consider
Similarly in
adding the two we get
or
Similarly we can have
and
adding the three we get
or
Hence, while perimeter of a triangle is greater than sum of its medians, sum of its medians is greater than half the perimeter.
In
Now
-
for
#DeltaABD#
#AD+BD>AB.....[1]# -
for
#DeltaBCE#
#BE+CE>BC.....[2]# -
for
#DeltaACF#
#CF+AF>CA.....[3]#
Adding [1],[2],[3] we get
So