<s>[INST] The area of a rectangle with length $5$ and width $3$ is $15$. Its diagonal, as a hypotenuse of the rectangle, can be found using the Pythagorean theorem with legs $3$ and $5$. The resulting answer is $$\sqrt{3^2 + 5^2} = \sqrt{34}.$$ Now, if we triple the length to get $15$ and correspondingly triple the width to get $9$ (since the ratio is $1:\frac{3}{5}$), we should obtain a new rectangle with an area $3^2$ or $9$ times greater than the original. Thus, the new rectangle's area should be $15 \times 9 = 135$, which makes sense since $15 \times 9 = 135$.
If this is true, then we could create a similar argument for any rectangle by scaling its dimensions while maintaining the ratio of the dimensions. Similarly, if we have a right triangle with legs $3$ and $5$ and hypotenuse $\sqrt{34}$, we should be able to create a similar triangle with scaled dimensions to get a similar right triangle, and the triangle must be right since the ratio of its legs stay the same. Thus, this must mean that $\boxed{\sqrt{x^2 + 9x}}$ is also the hypotenuse of a right triangle where $3x$ and $5x$ are the legs, but are the expressions $\boxed{\sqrt{x^2 + 9x}}$ and $\boxed{\sqrt{34}}$ equivalent?[/INST]