Chapter 12, Problem 18PTTS

To determine

To define : The expressions for the length and width of the rectangle’s image after dilation by a scale factor of 11.

Answer to Problem 18PTTS

The width of the image of rectangle after dilation $=\left(11\times x\right)=11x$ inches

Length of the image of rectangle after dilation $=\left\{11\times \left(x+2\right)\right\}=11x+22$ inches

Explanation of Solution

Given information : A rectangle is $2$ inches longer than its width. The scale factor for the dilation is $11$ .

Formula used : The scale factor of a dilation is the ratio of the side length of the image to the corresponding side length of the original figure.

Therefore, new length of the image after dilation $=$ scale factor $\times$ length of the original figure.

Calculation :

Let, the width of the rectangle is $x$ inches.

Therefore, the length of the rectangle $=\left(x+2\right)$ inches.

Here, the scale factor for the dilation is $11$ .

Therefore, the width of the image of rectangle after dilation $=\left(11\times x\right)=11x$ inches

Length of the image of rectangle after dilation $=\left\{11\times \left(x+2\right)\right\}=11x+22$ inches