Median Area

Geometry Level 3

If the medians of a triangle are 9 , 12 , 15 9,12,15 , with x x denoting its area. What is the value of x + 1927 x +1927 ?


The answer is 1999.

View wiki
Mehul Chaturvedi by Mehul Chaturvedi , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Rudresh Tomar
Nov 11, 2014

For the area of the triangle with sides of length u, v, and w. , the area of the triangle with medians of length u, v, and w is

s = ( 9 + 12 + 15 ) / 2 = 18 , u = 9 , v = 12 , w = 15 s = (9 + 12 + 15)/2 = 18, u = 9, v = 12, w = 15

x = 4 3 s ( s − u ) ( s − v ) ( s − w ) = 72 x = \frac 4 3 \sqrt{s(s-u)(s-v)(s-w)} = 72 , so x + 1927 = 1999 x+1927 = 1999

2 Helpful 0 Interesting 0 Brilliant 0 Confused

U r right Perfect formula but could u derive this

Mehul Chaturvedi - 6 years, 7 months ago

It's a right angled triangle so just use 1 2 × b × h \frac{1}{2}×b×h

Rohit Udaiwal - 5 years, 8 months ago
Shashank Atray
Nov 23, 2014

there is a very direct formulae for it but i dont know how to update pics here.... i will try to put it here understand that u, v, w are the length of medians 1/3(sqrt{(2(u^{2}*v^{2}+v^{2}w^{2}+u^{2}w^{2})-(u^{4}+v^{4}+w^{4})

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Mehul Chaturvedi
Nov 10, 2014

A direct formula can be used that is just LIKE herons formula

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you provide a complete explanation?

Also, did you mean that the area of the triangle is x?

Calvin Lin Staff - 6 years, 7 months ago

Log in to reply

Yes I have corrected that

Mehul Chaturvedi - 6 years, 7 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...