The probability can be determined by comparing the area of triangles XYZ and XYD. So that the probability is [tex]\frac{1}{3}[/tex].
A right angled triangle is a type of triangle that has one of its internal angles equal to [tex]90^{o}[/tex]. And the area of a triangle can be determined by;
Area of a triangle = [tex]\frac{1}{2}[/tex] x base x height
So that from the given question, area of triangle XYZ can be calculated as;
Area = [tex]\frac{1}{2}[/tex] 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) = [tex]\frac{12}{36}[/tex]
= [tex]\frac{1}{3}[/tex]
Thus, the probability that area of triangle XYD is at most 12 is [tex]\frac{1}{3}[/tex].
A sketch is attached to this answer for more clarifications.
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