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?

Guest Nov 27, 2019

#2**+1 **

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.

Melody Nov 27, 2019