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

`(xy)/(2)`

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

The new area is

`((3x)(3y))/(2) = (9xy)/(2) = 9(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.