​ help

Use the Pythgorean Thearom and find the hypotenuse remember a^2+b^2=c^2

divide RQ by 2 and divide PQ by 2 then use the Pythgorean Thearom to find ZX

Notice that $\triangle RYX \sim \triangle XZQ$ by AA postulate.

Let x be the side length of the square. Then

$ZQ = 12-x\\ RY=8-x\\ YX=x\\ XZ=x$

By similar triangles,

$\dfrac{RY}{YX} = \dfrac{XZ}{ZQ}\\ \dfrac{8-x}{x}=\dfrac{x}{12-x}$

Solving this equation gives the required answer.

Ans: Side length = 24/5.

As an exercise, you can try to show that when PQ = a, PR = b, the side length of the square is $\dfrac{ab}{a + b}$.