Sienna planned a trapezoid-shaped garden, as shown in the drawing below.

Question

A trapezoid has top side length of 4 inches, bottom side length of 9 inches, and left side length of 6 inches.
She decides to change the length of the top of the trapezoid-shaped garden from 32 ft to 24 ft. Which expression finds the change in the scale factor?
StartFraction 4 inches over 24 feet EndFraction
StartFraction 32 feet over 4 inches EndFraction
StartFraction 24 feet over 32 feet EndFraction
StartFraction 32 feet over 24 feet EndFraction

Answer 1

To find the change in the scale factor when Sienna changes the length of the top of the trapezoid-shaped garden from 32 ft to 24 ft, we need to determine the ratios of the new length to the old length.

The scale factor when comparing the new length (24 ft) to the original length (32 ft) can be calculated as:

\[ \text{Scale factor} = \frac{\text{new length}}{\text{original length}} = \frac{24 \text{ ft}}{32 \text{ ft}} \]

Among the options provided, the correct expression that finds the change in scale factor is:

\[ \frac{24 \text{ ft}}{32 \text{ ft}} \]

So the correct choice is:

StartFraction 24 feet over 32 feet EndFraction