MathDB

Let

ABC

be an equilateral triangle, and let

D

and

F

be points on sides

BC

and

AB

, respectively, with

FA=5

and

CD=2

. Point

E

lies on side

CA

such that

\angle DEF = 60^\circ

. The area of triangle

DEF

14\sqrt{3}

. The two possible values of the length of side

AB

are

p \pm q\sqrt{r}

, where

p

and

q

are rational, and

r

is an integer not divisible by the square of a prime. Find

r

Problem Statement