The width of a rectangle is doubled and its length is tripled. How many times larger is the area of the enlarged rectangle compared to the area of the original rectangle?
A. 6
B. 10
C. 12
D. 24
How many times larger is the area of the enlarged rectangle compared to the area of the original rectangle
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To find out how many times larger the area of the enlarged rectangle is compared to the original rectangle, we can follow these steps:
1. Calculate the area of the original rectangle:
– Let the original width be ( w ) and the original length be ( l ).
– The area ( A_{original} = w times l ).
2. Dimensions of the enlarged rectangle:
– The width is doubled: new width = ( 2w ).
– The length is tripled: new length = ( 3l ).
3. Calculate the area of the enlarged rectangle:
– The area ( A_{enlarged} = (2w) times (3l) = 6wl ).
4. Compare the two areas:
– To find how many times larger the area of the enlarged rectangle is compared to the original rectangle:
[
text{Ratio} = frac{A_{enlarged}}{A_{original}} = frac{6wl}{wl} = 6.
]
Thus, the area of the enlarged rectangle is 6 times larger than the area of the original rectangle.
The answer is A. 6.