Discussion
What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
Answer: D
All lengths in a square scale together: if the diagonal is three times larger, so is the side, and so is the perimeter.
\[ d = a\sqrt{2} \quad\Longrightarrow\quad \frac{d_{1}}{d_{2}} = 3 \;\Longrightarrow\; \frac{a_{1}}{a_{2}} = 3 \]
\[ \frac{P_{1}}{P_{2}} = \frac{4a_{1}}{4a_{2}} = 3 \quad\Longrightarrow\quad 3 : 1 \]
Only the areas would be squared, in the ratio 9 : 1. Perimeter, side and diagonal are all first powers of length and share one ratio.
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