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?


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Answer:

^@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 \%^@

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