Shortcuts

 Sitemap Contact Newsletter Store Books Features Gallery E-cards Games

•••

 Related links Puzzles workshops for schools & museums. Editorial content and syndication puzzles for the media & publishers. Numbers, just numbers facts & curiosities... Have a Math question? Ask Dr. Math!
•••

 ••• •••

•••

 Smile! "If I marry my aunt, I become my own uncle!" -- Voltaire Math Gems
•••

 ••• •••

Previous Puzzles of the Month + Solutions

Back to Puzzle-of-the-Month page | Home
Puzzle # 128

 Suggest to a friend Contact us Thumb up this page Share it on FaceBook Follow us on Twitter View our RSS feeds Digg this story
Xmas tree geometric puzzle

Find the value of h.

Difficulty level: , general math knowledge.
Category: Geometry.
Keywords: trapezium, trapezoid, base.
Related puzzles:
- Prof Gibbus' angle,
- Achtung minen.

 Français

Source of the puzzle:
© G. Sarcone.
You cannot reproduce any part of this page without prior written permission.
 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). Discuss the problem on our FaceBook page! © 2012 G. Sarcone, www.archimedes-lab.org You can re-use content from Archimedes’ Lab on the ONLY condition that you provide credit to the authors (© G. Sarcone and/or M.-J. Waeber) and a link back to our site. You CANNOT reproduce the content of this page for commercial purposes. You're encouraged to expand and/or improve this article. Send your comments, feedback or suggestions to Gianni A. Sarcone. Thanks!
 Previous puzzles of the month...
 Puzzle 127: Square vs Annulus (2011) Puzzle 126: A troublesome sequence (2011) Puzzle 125: A mathematical shield (2011) Apr-May 2010: A chopping problem Oct-Nov 09: The Mark of Zorro July-Sept 09: radiolarian's shell May-June 09: circle vs square Jan-Feb 09: geometric mouse Sept-Oct 08: perpendicular or not... July-Aug 08: ratio of triangles May-June 08: geometry of the bees Puzzle Archive
Back to Puzzle-of-the-Month page | Home
Recommend this page

 Information Services & Products Follow us via... Support us... • About Us • Privacy & Terms • Copyrights • Contact us • Sitemap • Press Review • Products • Features • Workshops • For Publishers • Facebook • Newsletter • RSS feeds • Twitter • Blogs • Tell a Friend • Merchandising • Link to us • Sponsorship © Archimedes' Laboratory™ | The web's best resource for puzzling and mental activitie | Introduzione | Introduction | Einführung