Question

A rectangle has a length of 9 inches and a width of 12 inches. This rectangle is dilated by a scale factor of 3.5 to create a new rectangle. Which figure represents the new rectangle.

Answer 1

divide both length and width by the dialtion factor and that will be the dimensions of the new rectangle. 2.5714in by 3.4286in. Round as needed

Answer 2

Answer : The figure of the new rectangle is shown below.

Step-by-step explanation :

As we are given that:

Length of rectangle = 9 inches

Width of rectangle = 12 inches

When the rectangle is dilated by a scale factor of 3.5 then it create a new rectangle.

Now we have to determine the figure of the new rectangle.

Formula of scale factor is:

$\text{Scale factor}=\frac{\text{Larger length}}{\text{Smaller length}}$

Given:

Scale factor = 3.5

The length of new rectangle will be:

$\text{Scale factor}=\frac{\text{Larger length}}{\text{Smaller length}}$

$3.5=\frac{\text{Larger length}}{9}$

$\text{Larger length}=3.5\times 9$

$\text{Larger length}=31.5$ inches

and,

The width of new rectangle will be:

$\text{Scale factor}=\frac{\text{Larger width}}{\text{Smaller width}}$

$3.5=\frac{\text{Larger width}}{12}$

$\text{Larger width}=3.5\times 12$

$\text{Larger width}=42$ inches

Thus, the figure of the new rectangle is shown below.