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 |.

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Last modified: June 18, 2007