The lengths of the medians through acute angles of a right-angled triangle are 3 and 4. Find the area of the triangle.

Explanation

AD=3

CE=4

Apollonian theorem

`(AB)^2+(AC)^2=2((AD)^2+(BD)^2)`

`b^2+c^2=2(9+a_2/4)-(1)`

`b^2+a^2=2(c^2/4+16)-(2)`

`b^2=a^2+c^2`

`2b^2+a^2+c^2=2(a^2/4+c^2/4+25)`

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