Question

find area of scalene triangle when its medians are 6cm 8cm 10 cm

Answer 1

Note that: Area of a triangle of medians is three-fourths of the area of the given triangle. So find the area of triangle of medians and then find the area of the triangle.
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Let the medians be a=10cm, b= 8cm and c = 6 cm.
If we form a triangle with these medians, the area of median triangle would be

$A= \sqrt{s(s-a)(s-b)(s-c)} \\ \\ where\ s= \frac {a+b+c}{2}\\ \\ s=\frac {10+8+6}{2}= \frac{24}{2}=12\\ \\ Area= \sqrt{12(12-10)(12-8)(12-6)}= \sqrt{12*2*4*6} \\Area= \sqrt{24*24}= 24\ cm^2$

$\frac{3}{4}* Area\ of\ actual\ triangle=Area\ of\ median\ triangle\\Area\ of\ actual\ triangle= \frac{4}{3}*Area\ of\ median\ triangle\\Area\ of\ actual\ triangle =\frac{4}{3}*24=\boxed {32\ cm^2}$