14 of 1514 of 15 Items Question Jorge draws a rectangle measuring 3 ft. by 2 ft. Then, he dilates the rectangle so it is 7.5 ft. by 5 ft. If x represents the area of the original rectangle, which expression can he use to discover the area of the dilated rectangle?(1 point) Responses x(1.5)2 x(1.5)2 x+(2.5)2 x+(2.5)2 x(2.5)2 x(2.5)2 Skip to navigation page 1 of 1

Answer 1

To find the area of the dilated rectangle, we first need to calculate the area of the original rectangle and the dilated one.

1. Original Rectangle:

   • Dimensions: 3 ft by 2 ft
   • Area \( x = 3 \times 2 = 6 \) square feet.

2. 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: \( x(2.5)^2 \)