The Magic of Pythagoras in an Unknown Rectangle !We all get used to using Pythagoras' Theorem with 2 numerical inputs, and an unknown 3rd 'length' to find. This Problem uses, instead, the algebra of the Theorem without the immediate substitution of numerical values ... until a bit of rearranging of the algebra has gone on ... The nice thing is that we aren't told, and don't need to know, the sides of the triangles concerned ! A Given a rectangular courtyard ABCD, and a well at the point P such that PA = 10, PB = 5 and  PC  = 11, then find PD. B
Given a rectangular box, and a point P such that  PA  = 13,  PB  = 5,
 PD  = 15 and 
PE  = 23, then find  PG . Open the File as a Word Document

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