This
is not a onesolution puzzle, as according to the
information given there is a range of possible
solutions.
a) The shape delimited on the Xmas tree forms
a trapezium/trapezoid.
b) The opposite angles of the lower base add
together and equal 90 degrees. Then, if we extend the
legs of the trapezium/trapezoid they will meet at an
angle of 90 degrees. All the possible 90degree angles
are inscribed in a semicircle (Thales’ theorem,
see diagram above). In consequence, the height h is
maximum when any of the angles of the lower base equals
45 degrees.
c) In this case, h_{max} =
(54 – 21)/2 = 16.5 [cm]
Thus,
the value x of h is: 16.5
[cm] > x > 0 [cm]
Geometric
terms
Trapezoid:
N. Amer. a quadrilateral with only one pair of parallel
sides.
Trapezium: Brit. a quadrilateral
with only one pair of parallel sides.
Base: one of the parallel
sides of the trapezium/trapezoid. Every trapezium/trapezoid
has two bases.
Leg: one of the sides of
the trapezium/trapezoid that are not parallel. Every
trapezium/trapezoid has two opposite legs.
