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?