The median is perpendicular to the hypotenuse, as it's an isosceles right triangle.
The ratio of sides is known, and triangle ABD ~ triangle ACB
AB/AC = BD/AB
AB/AC = 1/root(2) = 5/AB
AB = 5root(2)
BC = 5root(2)
So area of triangle ABC = 1/2 * 25 * 2 = 25
It is not clear if the median is perpendicular to the hypotenuse
The other sides are not known either.
Answer - A
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