### We draw a square inside a rectangle. The ratio of the rectangle's width to the square's side is $2:1$, and the ratio of the rectangle's length to its width is $4:1$. What percentage of the rectangle's area is inside the square?

$6.25 \%$

Step by Step Explanation:
1. Given, the ratio of the rectangle's width to the square's side is $2:1$.
Let the side of the square be $'a'$ units.
Therefore, the width of the rectangle $= 2 a.$
2. The ratio of the rectangle's length to its width is $4:1$.
So, the length of the rectangle $= 8 a$
3. Area of the rectangle inside the square $=$ Area of square
Area of square $= a^2$
Area of the rectangle $= 2 a \times 8 a = 16 a^2$
4. So, the percentage of the rectangle's area inside the square $= \dfrac{ \text{Area of the rectangle inside the square} } { \text{ Area of the rectangle } } \times 100$
$= \dfrac{ a^2 }{ 16 a^2 } \times 100 \%$
$= 6.25 \%$