Question 145860
Let the length of the sides be x

Draw in point D. Then label then label BD = x/3. That means DC = 2x/3

Now drop a vertical line from D that intersects AC at E. This forms two right triangles (DEC and ADE).

The angle C is 60 degrees. So triangle DEC has the hypotenuse DC with length 2x/3 and is a 30-60-90 triangle. Use trig to find the lengths of all three sides of DEC (2x/3,  x/3  and .866(2x/3) )

Now, since EC is x/3, then AE is 2x/3. DE is ,866(2x/3). ADE is also a right trianlge. You have two sides, so you can use pythagorean theorem to find the third side.

Doing so yields AD^2 = (2x/3)^2 + (0.866(2x/3))^2 = 1.75 (4/9)x^2 = (7/9)x^2