Final answer:
To determine the length of Katie's reduced rectangular design, a scale factor is calculated from the new and original widths, then applied to the original length. The new length is found to be 8.1 inches.
Step-by-step explanation:
Katie has a rectangular design that she wants to reduce at Kinko's Copy Center. To find the new length of the reduced design when the width is changed from 32 inches to 6.4 inches, we must first determine the scale factor. The scale factor can be calculated by dividing the new width by the original width, which is:
Scale factor = New width / Original width = 6.4 inches / 32 inches = 0.2
Once we have the scale factor, we use it to find the new length of the rectangular design:
New length = Original length x Scale factor
New length = 40.5 inches x 0.2 = 8.1 inches
Therefore, the length of the reduced design is 8.1 inches.