000RM.dvi

3.2 Construction of equilateral triangle inscribed in a rectangle 119

3.2 Construction of equilateral triangle inscribed in a

rectangle

What is more interesting is that the above calculation leads to a very easy
construction of the equilateral triangleAXY.

Construction 3.1. Construct equilateral trianglesBCY andCDXso
thatXandY are in the interior of the rectangle.^1 JoinAXto intersect
BCatPandAYto intersectCDatQ. ThenAXY is equilateral.

P

Q

A B

D C

X

Y

M

N

(^1) This is not always possible. What is the range of the ratioabforXandYto be in the interior of the
rectangle?