Geometry Problem
Click the figure below to see the complete problem 540 about Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras.
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Tuesday, November 9, 2010
Problem 540: Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras
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Denote length AC = b, length BC = a (assume a>b)
ReplyDeleteExtend NB to meet HD at X;
Extend AG to meet BX at Y.
Easy to derive GH = HX = a - b,
XD = BF = b,
DF = XB = a,
A3 = Area of rectangle ACBY
+ Area of rectangle BFDX
+ Area of square GHXY
= ab + ab + (a-b)^2
= a^2 + b^2
= A1 + A2