Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. What is the probability that the area of triangle XYD is at most ?
The probability that the area of triangle XYD is at most is 1/2. This is because the area of a right triangle is equal to 1/2 the product of the lengths of the two legs. Since the lengths of the two legs of triangle XYZ are known, the area of any triangle XYD within triangle XYZ will be at most 1/2 the product of the lengths of the two legs.
