Question

The triangle ABC has medians AD, BE, CF, AD lies along the line $y=x+3$, BE lies along the line $y=2x+4$, AB has length $60$ and angle $C={90}^o$, then the area of $\Delta$ABC is?

• A. $400$
• B. $200$
• C. $100$
• D. None of these

Answer 1

Answer: (A)

$400$

The easiest way to solve this question is by shifting the centroid to origin.

Thus now equations of median are $y=x$ and $y=2x$.

Now the coordiantes of $A$ can be taken as $(a,a)$ and that of $B$ can be taken as $(b,2b)$

Using centroid formula $C(-a-b,-a,-2b)$

Equate hypotenuse length equal to $60$ get one equation. Second equation comes from slope of $AC$ and $BC$ product is $-1$. Solving both the equations you will get $ab=(-800/3)$.

Find out area of triangle using all three co-ordinates. Area $=3/2\left(ab\right)=400$