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There is a point X inside a square PQRS such that PX = 1, QX = 2 and triangles PXQ and PXS are congruent. What is the area, in square units, of the square?

 Nov 27, 2019

I will give you some hints:

THIS is not all the working that you need.  It is just an outline.


Draw the pic.  Keep drawing new pics, as you need to,  if you get more information.


A square is a special type of rhombus.  What is the forrmula for the area of a rhombus?


Any point on the diagonal of a square will be equidistant to the other two vertices so X must be on the diagonal PR


Let the diagonal have length 2d   SO half the diagonal is  d

Let the centre of the square be C


From that info you can work out distance XC in terms of d


Now use pythagoras's theorum in triangle XQC  to set up an equaton in d.    Now solve for d.


Once you have d you can work out the area of the square.

 Nov 27, 2019

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