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

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 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
askIITians Faculty

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