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 12?

The probability can be determined by comparing the area of triangles XYZ and XYD. So that the probability is .

A right angled triangle is a type of triangle that has one of its internal angles equal to . And the area of a triangle can be determined by;

Area of a triangle = x base x height

So that from the given question, area of triangle XYZ can be calculated as;

Area = x 6 x 12

        = 3 x 12

        = 36

The area of triangle XYZ is 36 square units.

Given triangle XYD, the probability that its area is at most 12 is;

Pr(area of triangle XYD is at most 12) =

                                                             =

Thus, the probability that area of triangle XYD is at most 12 is .

A sketch is attached to this answer for more clarifications.

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