+311 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 24?
+29 The area of the triangle is (12 * 6)/2 = 36.
The area formula for a triangle is 1/2 * bh.
We already know the base; it is XY, which is 12.
So, 1/2 * 12 * h is less than or equal to 24.
This is only true when h is less than or equal to 4, in which the altitude from D to XY is less than 4.
So, the area of the triangle that does not satisfy this condition has height 2 and base 4, which works out to an area of 4.
So, the chance of faliure is 4/36 = 1/9, and the chance of success is 1 - 1/9 = 8/9.
