This week's maths problem

Problem of the week

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On Friday of each week we will post a new maths challenge.
You may submit your solution by the following Thursday.
Each problem contains two different levels of difficulty. You will be awarded from 2 to 12 points for a full answer.
Each series contains 12 problems before the stage winner is determined.
Your score will be published here.

In each series we will give away 3 books as prices. The prices will be drawn by lot among the best ten participants of the series. The books are kindly sponsored by Buchdienst Rattei of Chemnitz.

Suggestions for problems are welcome.

Deadline is 19th October 2017.

German version - Italian version - French version - Spanish version

 

Series 46

problem 544

544

“That looks like an illustration of Pythagoras’ theorem”, Mike said.
“Of course it does. Triangle ABC is right-angled (a=3cm, b=4cm and c=5cm.) The quadrangles are squares.”
How long would a cord have to be if it was stretched tightly around the shape? (Caclulating the length 8 blue points, solution by construction: 4 blue points.)
The shape fits into square WXYZ whose sides are equal to the distance between I and J. How big (length of sides) would this square be and how many percent of its area would be covered by the illustration of Pythagoras’ theorem? - 4 red points. If you find a way of construction a square smaller than WXYZ but still competely containing the Pythagoras shape you will be awarded another 6 red points. These points will likewise be given if shown that none such square exists.

               


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You can also send a paper copy of your solution as long as it is postmarked on or before the deadline.
adress:
Thomas Jahre
Stollberger Strasse 25
09119 Chemnitz
Germany


Links:

http://www.wurzel.org/

https://www.facebook.com/ArchimedesLab

http://people.missouristate.edu/lesreid/potw.html

post address:

Thomas Jahre
Chemnitzer Schulmodell
Stollberger Straße 25
09119 Chemnitz
Deutschland/Germany
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