Chapter 5.8, Problem 20HP

To determine

To find: The area of the new rectangle if the rectangle $ABCD$ is reduced by a scale factor of $\frac{1}{2}$ .

Answer to Problem 20HP

The area of the new rectangle is $12\text{in}{\text{.}}^2$ .

Explanation of Solution

Given information:

The given rectangle is shown below.

  

Calculation:

From the figure, the area of the rectangle $ABCD$ is $48\text{in}{\text{.}}^2$ . Let the new rectangle is $WXYZ$ .

  

Since, the rectangle $ABCD$ is reeducated by a scale factor $\frac{1}{2}$ . When a rectangle is reduced by a scale factor, the new formed rectangle is similar only the dimensions of the rectangle is reduced.

The area of the new rectangle $WXYZ$ can be calculatedby dividing the area of the rectangle $ABCD$ with the square of the scale factor.

Calculate the square of the scale factor.

  ${\left(\frac{1}{2}\right)}^2=\frac{1}{4}$

Calculate the area of the new rectangle $WXYZ$ .

  $48\text{in}{\text{.}}^2\times \frac{1}{4}=12\text{in}{\text{.}}^2$

Therefore, the area of the new rectangleis $12\text{in}{\text{.}}^2$ .