perplexus.info :: Shapes : Pair of Quadrilaterals

Pair of Quadrilaterals (Posted on 2006-02-17)

Harry and Tom each drew a quadrilateral such that when lines were drawn from each of its vertices to a point within it to divide it into four triangles, the angles at the central point in each case, in order, were 60 degrees, 120 degrees, 90 degrees and 90 degrees.

All the sides of the triangles were an integral number of centimeters, and no side exceeded 20 cm.

The perimeter of Harry's quadrilateral was longer than Tom's. How much longer was it?

Submitted by Charlie

Rating: 4.0000 (2 votes)

Solution: (Hide)

The lengths of the central "spokes" appear on the left below, alternating with (indented) angle between them. On the angle line is also the outer side of the triangle, and therefore the quadrilateral.
The respective totals appear below each of the two sets.

5
120 19
16
90 20
12
90 13
5
60 5
5
----
57

16
120 19
5
90 13
12
90 20
16
60 16
16
----
68

The larger perimeter is 68 cm and the smaller is 57, for a difference of 11.
This puzzle adapted from New Scientist's Enigma number 1370, in the 10 December 2005 issue.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Answer	K Sengupta	2008-12-07 00:45:27
Second Quadrilateral and Solution	Eric	2006-02-17 16:45:10
First Quadrilateral	Eric	2006-02-17 16:35:10

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