Two medians drawn from acute angles of a right angled triangle intersect at an angleπ/6 . If the length of the hypotenuse of the triangle is 3 units, then area of the triangle (in sq. units) is

Let A(a,0) and B(0,b) then G=a3,b3Slope of is AN = -b2a  and slope of BM = -2ba Now if θ is the angle between the medians then tanθ=m1-m21+m1m2tan300= -b2a--2ba1+-b2a-2ba =3b2a1+b2a2    ⇒13=3ba2(a2+b2)                                                                                   ⇒12ab=(a2+b233)      taking a2+b2=9ab=23Area of the triangle = 12ab=12×23=3