A rectangle is reduced by a scale factor of One-fourth. A large rectangle has a length of 16 and width of 12. A smaller rectangle has length of 4 and width of 3. Which choices show the ratio of the area of the smaller rectangle to the area of the larger rectangle? Select three options. StartFraction 4 over 16 EndFraction (StartFraction 4 over 16 EndFraction) squared StartFraction 12 over 192 EndFraction StartFraction 4 squared over 12 squared EndFraction (StartFraction 3 over 12 EndFraction squared
Question
A rectangle is reduced by a scale factor of One-fourth.
A large rectangle has a length of 16 and width of 12. A smaller rectangle has length of 4 and width of 3.
Which choices show the ratio of the area of the smaller rectangle to the area of the larger rectangle? Select three options. StartFraction 4 over 16 EndFraction (StartFraction 4 over 16 EndFraction) squared StartFraction 12 over 192 EndFraction StartFraction 4 squared over 12 squared EndFraction (StartFraction 3 over 12 EndFraction squared
Solution
The area of a rectangle is calculated by multiplying its length by its width.
For the larger rectangle, the area is 16 * 12 = 192 square units.
For the smaller rectangle, the area is 4 * 3 = 12 square units.
The ratio of the area of the smaller rectangle to the area of the larger rectangle is therefore 12/192.
This simplifies to 1/16, which is the same as StartFraction 4 over 16 EndFraction.
The square of the scale factor (1/4) is (1/4)^2 = 1/16, which is the same as (StartFraction 4 over 16 EndFraction) squared.
The ratio of the squares of the lengths of the rectangles is (4^2) / (16^2) = 16/256 = 1/16, which is the same as StartFraction 4 squared over 16 squared EndFraction.
So, the correct options are:
StartFraction 4 over 16 EndFraction (StartFraction 4 over 16 EndFraction) squared StartFraction 4 squared over 16 squared EndFraction
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