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)

Question

Responses

x(1.5)2
x left parenthesis 1.5 right parenthesis squared

x(2.5)2
x left parenthesis 2.5 right parenthesis squared

x+(2.5)2
x plus left parenthesis 2.5 right parenthesis squared

x(2.5)

Answer 1

The area of a rectangle is calculated by multiplying its length and width. The original rectangle has dimensions of 3 ft by 2 ft, so its area \( x \) is:

\[ x = 3 \times 2 = 6 , \text{ft}^2 \]

After dilation, the new dimensions of the rectangle are 7.5 ft by 5 ft. We can find the scale factor of the dilation by comparing the corresponding dimensions of the original and dilated rectangles.

The scale factor for the length is:

\[ \frac{7.5}{3} = 2.5 \]

The scale factor for the width is:

\[ \frac{5}{2} = 2.5 \]

Since both dimensions scale by the same factor, we can use this scale factor to find the area of the dilated rectangle. The area of the dilated rectangle is given by the area of the original rectangle multiplied by the square of the scale factor:

\[ \text{Area of the dilated rectangle} = x \times (2.5)^2 \]

Therefore, the correct expression to discover the area of the dilated rectangle is:

x(2.5)² or x(2.5) squared.