Where is The Book solution? Writing AB = a, BC = b, DP = x, DQ = y, and noting that an affine transformation needn't change the areas, so that we can assume that the parallelogram is a rectangle, we have a(b-y) = 12, b(a-x) = 58, xy = 34, ab = 52+A, where A is the required area. The first two (with the last) give ay = A + 40, bx = A - 6 Multiplying the last two pairs of equations, 34(A+52) = (A+40)(A-6), A^2 = 2008 but how does one SEE what is going on ??? [the last equation is 4-dimensional!] R. On Thu, 13 Dec 2007, Schroeppel, Richard wrote:
A New Year's Puzzle that's been circulating here ...
B--------------C /|\_ / / / \_ 29 / / | \_ / / / \_ / / | ? \/ / / __--P / 6 | __-- / / /_-- 17 / A----Q---------D
ABCD is a parallelogram. P is on CD, Q is on AD. The areas of the triangles ABQ, BCP, and PDQ, are 6, 29, and 17. What's the area of triangle BPQ?
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