(1)

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

Sufficient

(2)

It is not clear if the median is perpendicular to the hypotenuse

The other sides are not known either.

Not Sufficient

Answer - A

Attachments

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