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?
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.