What scale factor was used to enlarge the rectangle in the image? The measurements refer to inches. Give your answer as a decimal.

Question

small rectangle measurements are 3 inches and 5 inches
Big rectangle measurements are 5.4 inches and 9 inches

Answer 1

To find the scale factor used to enlarge the rectangle, you can compare the corresponding side lengths of the small rectangle and the big rectangle.

For the length:

• Small rectangle length: 5 inches
• Big rectangle length: 9 inches

Scale factor for length: \[ \text{Scale Factor} = \frac{\text{Big rectangle length}}{\text{Small rectangle length}} = \frac{9}{5} = 1.8 \]

For the width:

• Small rectangle width: 3 inches
• Big rectangle width: 5.4 inches

Scale factor for width: \[ \text{Scale Factor} = \frac{\text{Big rectangle width}}{\text{Small rectangle width}} = \frac{5.4}{3} = 1.8 \]

Both the length and the width give the same scale factor of 1.8.

Therefore, the scale factor used to enlarge the rectangle is \( \boxed{1.8} \).