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 $1.$

13.44%

Step-by-step explanation:

For DG to have length of 1 or less, point G must be contained in a sector of a circle with center at point D, radius of 1, and a central angle of 60°.

The area of that sector is

The area of the triangle is

The probability is the area of the sector divided by the area of the triangle.

70

step-by-step explanation: