# Can you square root the sides of a proportional right Triangle?

I am working on this question, and the solution says something weird.

Here is the question :

The solution starts by saying

The part I don't get is where they say 'PQR is $$9 = 3^2$$ to $$1$$, so the ratio is $$3$$ to $$1$$'. How can you square root each side of a triangle and keep it proportional to the other? If you multiplied each side by a number like $$4$$, the proportionality would stay the same, but if you squared or square rooted, wouldn't the triangles be no longer proportional?

Thanks for the help!

• Read carefully: proportion $9:1$ is referred to the areas of triangles. And areas are indeed proportional to the squares of lengths. – Aretino Feb 10 at 15:12