Question

A rectangle with a length of 3 centimeters and width of 2 centimeters is enlarged. The new perimeter is 510 centimeters. What scale factor was used to enlarge this rectangle?

A. 255
B. 170
C. 102
D. 51

Answer 1

The rectangle was enlarged by a scale factor of 51 to reach a perimeter of 510 centimeters, corresponding to option D.

Step-by-step explanation:

To find the scale factor used to enlarge a rectangle from a length of 3 centimeters and a width of 2 centimeters to a new perimeter of 510 centimeters, first calculate the original perimeter:

Original Perimeter = 2 * (length + width) = 2 * (3 cm + 2 cm) = 2 * 5 cm = 10 cm.

Now, since the enlarged rectangle has a perimeter of 510 cm, we divide the new perimeter by the original perimeter to find the scale factor:

Scale Factor = New Perimeter / Original Perimeter = 510 cm / 10 cm = 51.

Therefore, the rectangle was enlarged by a scale factor of 51, which corresponds to option D.