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In the diagram below, P is a point inside square ABCD.  Find x.

 

 May 10, 2023
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The diagonals of a square are equal and bisect each other at right angles

 

Therefore, angle APB is a right angle and the triangle APB is an isosceles right triangle with sides of 1.

 

By Pythagoras' Theorem:

 

x^2 = 1^2  +  1^2

x^2 = 2

x =sqrt(2) = 1.41421.....

 May 10, 2023

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