Question

In a triangle $ABC$ if the equation of the medians $AD$ and $BE$ are $2x+3y-6=0$ and $3x-2y-10=0$ respectively and $AD=6,BE=11$ , then the area of triangle $ABC$ , is

• A. $1$
• B. $22$
• C. $\frac{44}{3}$
• D. $44$

Answer 1

Answer: (D)

Let $G$ is centroid $AG=\frac{2}{3}AD=\frac{2 \times 6}{3}=4$
$BG=\frac{2}{3}BE=\frac{2 \times 11}{3}=\frac{22}{3}$
Area of $\Delta ABC=3\times $ (Area of $\Delta AGCB$ )
$=3\times \left(\frac{1}{2} \times 4 \times \frac{22}{3}\right)$
$=44squnit$