Let DEF be an equilateral triangle with side length 3. At random, a point G is chosen inside the triangle. Compute the probability that the length $DG$ is less than or equal to \(2\)

 Feb 24, 2022

First one.

If DG is at most one, we can draw a circle with radius 1 and center D.

We know the circle and triangle will share a 60 degree sector (because equilateral triangles have angle 60 degrees each).

So the area of the sector is pi/6.

The area of the entire equilateral triangle is sqrt3/4*a^2, and since a=3, 9sqrt3/4.

3.8971 is the approx. area of triangle

0.5236 is the approx. area of sector.

So 0.5236/3.8971 is around 0.134356

Or 13.4356%.

 Feb 25, 2022

Nice attempt Kakashi.


I used the same logic but I think you made some careless errors.   (then again maybe it was me.)

Melody  Feb 25, 2022
edited by Melody  Feb 25, 2022

The same logic leads to the right answer, but Kakashi read the problem wrong. They taught it was within 1 cm, not 2. 

BuilderBoi  Feb 25, 2022

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