question_answer

The medians of a \[\Delta ABC\] are 9 cm, 12 cm and 15 cm respectively. Then the area of the triangle is -

A) 96 sq. cm

B) 84 sq. cm

C) 72 sq. cm

D) 60 sq. cm

Correct Answer: C

Solution :

Produce the median AM to D such that

GM=MD

And join to B and C.

Now GBDC is a parallelogram. Note that the sides \[\Delta GDC\] of the are 6,8,10

\[\Rightarrow \angle GDC=90{}^\circ \]

\[\left. \begin{matrix}    Area\,\,of\,\,\Delta \,ADC=\frac{12.8}{2}=48  \\    Area\,\,of\,\,\Delta \,MDC=\frac{3.8}{2}=12  \\ \end{matrix} \right]\]\[\Rightarrow Area\,\,of\,\,\Delta \,AMC=36\]\[\Rightarrow Area\,\,of\,\,\Delta \,ABC=72\,c{{m}^{2}}]\]