Please solve q 106 ?
3 Answers
Explanation:
As shown in the figure,
draw a line
as
as
Now,
as
similarly,
Now, see Fig 2,
let
Now, use Heron's formula to find
where
and
AD, BE and CF are three medians of
Hence
So
Similarly
Again
Hence in
So if each side of
[By Heron's formula it can be shown that the increase of each side of triangle by m times will increase the area of the triangle by
Again
So
Now using Heron's formula we can get area of
we have
semi perimeter
So
Hence
I got in general
Explanation:
I didn't peek at the other answers. Let's try a direct approach and figure out the lengths of the medians. Can we do it in general.
Triangle sides
I recognize the numerator as sixteen times the squared area of the triangle. Even if you didn't we can see it because we know the area of the triangle is
So in passing we found a formula for the area of a triangle given the sides. I'll write it out the variants in full for reference.
One of these is almost always better than Heron.
Back to the problem. For sanity we'll write
We have triangle
The midpoints of the sides are
The median squared lengths are
Let's call the area of the median triangle
That simplified nicely.