# if median of triangle are 5 cm 6cm and 7cm then find area of this triangle.

Jitender Singh IIT Delhi
8 years ago
Ans:
Let the median length be m1, m2& m3. Then area of triangle A is:
$A = \frac{4}{3}\sqrt{S(S-m_{1})(S-m_{2})(S-m_{3})}$
where S is
$S= \frac{m_{1}+m_{2}+m_{3}}{2}$
$S= \frac{5+6+7}{2} = 9$
$A = \frac{4}{3}\sqrt{S(S-m_{1})(S-m_{2})(S-m_{3})}$
$A = \frac{4}{3}\sqrt{9(9-5)(9-6)(9-7)}$
$A = \frac{4}{3}\sqrt{9.4.3.2}$
$A = 8\sqrt{6}$
Thanks & Regards
Jitender Singh
IIT Delhi