MathDB

Draw an equilateral triangle with center

O

. Rotate the equilateral triangle

30^\circ, 60^\circ, 90^\circ

with respect to

O

so there would be four congruent equilateral triangles on each other. Look at the diagram. If the smallest triangle has area

1

, the area of the original equilateral triangle could be expressed as

p+q\sqrt r

where

p,q,r

are positive integers and

r

is not divisible by a square greater than

1

. Find

p+q+r

Problem Statement