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 of the

\[\Delta \,GDC\]are 6, 8, 10 \[\Rightarrow \]\[\angle GDC=90{}^\circ \]

\[\left. \begin{matrix}    \begin{matrix}    Area\,\,of\,\,\Delta \,ADC=\frac{12.8}{2}=48  \\    Area\,\,of\,\,\Delta \,MDC=\frac{3.8}{2}=12  \\ \end{matrix}  \\ \end{matrix} \right]\]

\[\Rightarrow \] Area of \[\Delta \,AMC=36\]

\[\Rightarrow \] Area of \[\Delta \,ABC=72\,\,c{{m}^{2}}\]