To find the area of the dilated rectangle, we first need to calculate the area of the original rectangle and the dilated one.
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Original Rectangle:
- Dimensions: 3 ft by 2 ft
- Area \( x = 3 \times 2 = 6 \) square feet.
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Dilated Rectangle:
- Dimensions: 7.5 ft by 5 ft
- Area = \( 7.5 \times 5 = 37.5 \) square feet.
To find the scaling factor for the area, you can note the change in the dimensions:
- The length changes from 3 ft to 7.5 ft, which is a factor of \( \frac{7.5}{3} = 2.5 \).
- The width changes from 2 ft to 5 ft, which is also a factor of \( \frac{5}{2} = 2.5 \).
Since the area of similar figures changes by the square of the scaling factor, we take the scaling factor (2.5) and square it:
\[ (2.5)^2 = 6.25 \]
Thus, the dilated area can be expressed in terms of the original area \( x \):
\[ \text{Area of dilated rectangle} = x \times 6.25 \]
Now, since \( 6.25 \) can also be expressed as \( (2.5)^2 \):
The correct expression Jorge can use to discover the area of the dilated rectangle is:
Answer: \( x(2.5)^2 \)