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 \(2\)

Guest Feb 24, 2022

#1**-1 **

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%.

Kakashi Feb 25, 2022

#3**+1 **

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