This
is not a one-solution 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 90-degree 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, hmax =
(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.
The
Winner of the Puzzle of the Month is: Gordon Steadman, Canada
Congratulations!
Beyond
the challenge (#128bis)
A
small change has been made to the statement of the
above-mentioned math problem: ABCD is a trapezium/trapezoid
α ≠ 45° AB = 21 [cm] DC = 54 [cm] AJ = JB and DK = KC
Now, find the value x of JK (this
is a one-solution puzzle! See diagram below).
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Puzzle
# 128
,
general math knowledge.
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