Let triangle $DEF$ be equilateral, where the side length is $3.$ A point $G$ is chosen at random inside the triangle. Find the probability that the length $DG$ is at most $1.$

13.43%

Step-by-step explanation:

see the attached figure to better understand the problem

we know that  

The probability that a point selected a random in triangle has distance from D to 1 or less is given by the area of the sector divided by the area of triangle

step 1

Find the area of sector

we have

substitute

step 2

Find the area of triangle

Applying the law of sines

The area of an equilateral triangle is equal

we have

step 3

Find the probability

substitute

assume

Convert to percentage