Problem Solving

[GMAT math practice question] 6.10

A 30-60-90 triangle is drawn on the exterior of equilateral triangle ABC as shown in the figure below so that the hypotenuse of the right triangle forms one side of the equilateral triangle. If the length of CD is 2, what is the length of AD?



A. 3
B. 4
C. 5
D. √7
E. 2√7

=>

Since the triangle BCD is a 30-60-90 triangle, CD:BC:BD = 1 : 2 : √3.
So, BC = 4, AB = 4, and BD = 2 √3.
Angle ABD is a right angle since angle ABC is 60 degrees, and angle CBD is 30 degrees.
By Pythagoras' theorem, AD^2 = AB^2 + BD^2 = 16 + 12 = 28. Therefore, AD = 2√7.

Therefore, E is the answer.
Answer: E