### Instruction: Solve for $r$: $r = \displaystyle\frac{\sqrt{5^2+12^2}}{\sqrt{16+9}}$. Express as a common fraction.### Response: I notice that the numerator and denominator of the fraction are both square roots of sums of squares, so I wonder if I can use the Pythagorean theorem somehow.
I see that $5^2+12^2 = 13^2$, so the numerator is $\sqrt{13^2} = 13$.
I also see that $16+9 = 25$, so the denominator is $\sqrt{25} = 5$.