Question

A rectangular picture has dimensions 2½ by 1½. it is to be enlarged so that it is still similar to the original rectangle. if the longer dimension is now 10, how much longer than the original is the perimeter now?

a. 3.5 times
b. 4 times
c. 2.5 times
d. 3 times

Answer 1

To find the new perimeter of the enlarged rectangle, divide the longer dimension of the enlarged rectangle by the longer dimension of the original rectangle. Then multiply the original perimeter by the scale factor to find the new perimeter. The new perimeter is 4 times longer than the original perimeter.

Step-by-step explanation:

To find the new perimeter of the enlarged rectangle, we need to first find the new dimensions of the rectangle. Since the longer dimension of the original rectangle is 2½ and the longer dimension of the enlarged rectangle is 10, we can find the scale factor by dividing the longer dimension of the enlarged rectangle by the longer dimension of the original rectangle: 10/2½ = 10/(5/2) = 10 × 2/5 = 4.

Therefore, the scale factor is 4, which means the new dimensions are 4 times larger than the original dimensions. Since the original perimeter is 2½ + 2½ + 1½ + 1½ = 8, the new perimeter is 4 × 8 = 32.

Therefore, the new perimeter is 32, which is 4 times longer than the original perimeter. The answer is (b) 4 times.