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?

The other quadrilateral is made up of the same right triangles but now has an equilateral triangle 16-16-16 and the obtuse triangle is 5-16-19

The two quadrilaterals only differ by the side length of their equilateral triangles, 16-5 or 11.

 

Posted by Eric on 2006-02-17 16:45:10