MthT 491 Geometric Proportional Reasoning
MthT 491 Geometric Proportional Reasoning
From Math Olympics - Rome, March 21, 1997:
1.
In the unit square ABCD the points P, Q, R, S are the midpoints of the sides. What is the ratio between the area of the smaller square JKLM and the area of the square ABCD?

squarem.gif

2.
(A general problem) In the unit square ABCD the points P, Q, R, S on th sides such that the proportions AP:AD = DS:DC = CR:CB = BQ:BA = a. What is the ratio between the area of the square JKLM and the area of the square ABCD?

squarea.gif



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On 18 Nov 2003, 09:10.