Question

How does tripling the side lengths of a right triangle affects its area?

Answer 1

Let $x,y$ be the lengths of the original legs. The original area is thus

$\dfrac{xy}{2}$

Now, we triple the legs, so we have $(x,y)\mapsto(3x,3y)$

The new area is

$\dfrac{(3x)(3y)}{2} = \dfrac{9xy}{2} = 9\dfrac{xy}{2}$

which is 9 times the original area.

So, if you triple both legs, the area will be nine times as much as the original one.