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
Hey can someone pls just say a simple sentence like this...
Hey here's the answer to ur question in edgenuity
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The answer is 4/16^2
To find the ratio of the area of the smaller rectangle to the area of the larger rectangle, we need to calculate the area of each rectangle and then divide the area of the smaller rectangle by the area of the larger rectangle.
The formula for the area of a rectangle is length times width.
For the larger rectangle with a length of 16 and width of 12, the area is 16 * 12 = 192.
For the smaller rectangle with a length of 4 and width of 3, the area is 4 * 3 = 12.
Now, let's look at the given options:
1. StartFraction 4 over 16 EndFraction:
This is the ratio of the length of the smaller rectangle to the length of the larger rectangle, not the ratio of their areas. Incorrect.
2. (StartFraction 4 over 16 EndFraction) squared:
This is the square of the ratio of the length of the smaller rectangle to the length of the larger rectangle, not the ratio of their areas. Incorrect.
3. StartFraction 12 over 192 EndFraction:
This is the correct ratio, as it is the area of the smaller rectangle (12) divided by the area of the larger rectangle (192).
4. StartFraction 4 squared over 12 squared EndFraction:
This is the square of the ratio of the length of the smaller rectangle to the width of the larger rectangle, not the ratio of their areas. Incorrect.
5. (StartFraction 3 over 12 EndFraction) squared:
This is the square of the ratio of the width of the smaller rectangle to the width of the larger rectangle, not the ratio of their areas. Incorrect.
Therefore, the correct choices for the ratio of the area of the smaller rectangle to the area of the larger rectangle are:
- StartFraction 12 over 192 EndFraction
I'll ignore all that wordy text formatting stuff, and cut to the chase.
The area scales as the square of the linear ratio, which is 4/16 (or 3/12).
So, ...