PRIZE PUZZLE FOR NOVEMBER 2007

DIAGONALS

I have a rectangular block of wood (that is, each of the six faces are rectangles). The diagonals across the faces measure exactly 40, 43 and 51 mm. What is the length of the diagonal across the centre of the block?

Send your answer to me, David Broughton.
Click this symbol for my email address.
Closing date: 5th December 2007.
Answer 
If A,B,C are the squares of the three sides, the answer is the
square-root of A+B+C.  We don't need to work out the sides, which
are irrational numbers.

Pythagoras tells us that:

    A+B   = 40 x 40 = 1600
      B+C = 43 x 43 = 1849
    A  +C = 51 x 51 = 2601

Adding these three equations:

    2A+2B+2C = 1600+1849+2601 = 6050
halving
     A+B+C = 3025
so the answer is the square root of 3025 which is 55.

I received only one answer, from John Stafford, so there was no draw this month. Thanks to John for his analysis of the problem.

[home] [back]