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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?

 May 16, 2024
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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.

 May 17, 2024

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