A triangle ABC has length AB=10cm and medians from A and B are 9 and 12 cm respectively. Find the area of the triangle.

we know that medians intersect such that they are divided in the ratio of  2:1. let the medians intersect at O. so 9 and 12 would be divided as 6:3 and 8:4.

hence we will have a triangle ABO with sides 6, 8, 10, which is right angled. so we can find sine(OAB)= 8/10.

now a median divides a triangle in two parts of equal areas. so total area of triangle= 2*area of triangle formed by median 9= 2*(½)*10*9*sin(OAB)= 90*8/10

=72 sq units