Question

Two medians drawn from acute angles of a right angled triangles intersect at an angle `pi//6`. If the length of the hypotenuse of the triangle is 3 units, then area of the traingle (in sq. units) is
A. `sqrt(3)`
B. 3
C. `sqrt(2)`
D. 9

Comments

Thanks

Answer 1

Correct Answer - A
`because " "AC=3impliesa^(2)+b^(2)=9`
Slope of `AD=(-2b)/(a)`
Slope of `CF=(-b)/(2a)`
`therefore" "tan.(pi)/(6)=|(-(2b)/(a)+(b)/(2a))/(1+(b^(2))/(a^(2)))|=|(-3ab)/(2(a^(2)+b^(2)))|=(3ab)/(9xx2)=(1)/sqrt(3)=(ab)/(6)impliesab=2sqrt(3)`
`DeltaABC = (1)/(2)ab=sqrt(3)`