Ratio of sides 2

The ratio of the side lengths of one square to another is 1:2. Find the ratio of the area of the two squares.

Correct answer:

r =  1:4

Step-by-step explanation:

$$\begin{gathered} a_1=1 \\ {a}_2=2 \\ k=a_1\mathrm{/}{a}_2=1\mathrm{/}2={\displaystyle \frac{1}{2}}=0.5 \\ {S}_1=a_1^2 \\ {S}_2=a_2^2 \\ r=S_1\mathrm{/}{S}_2=a_1^2:a_2^2=(a_1:a_2{)}^2=k^2 \\ r=k^2=0.5^2={\displaystyle \frac{1}{4}}=0.25=1:4 \end{gathered}$$

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