Question

A rectangle with a perimeter of 48 units is the image of a rectangle that was dilated by a scale factor of start fraction, 3, divided by, 2, end fraction
2
3
​
. Find the perimeter of the preimage, the original rectangle, before its dilation. Round your answer to the nearest tenth, if necessary.
Answer
Attempt 1 out of 2

units units
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Answer 1

Perimeters scale by the same factor as linear dimensions. If k is the scale factor (image = k × preimage), then

P_preimage = P_image / k.

- If the scale factor is 2/3, then P_preimage = 48 ÷ (2/3) = 48 × (3/2) = 72 units.
- If the scale factor is 3/2, then P_preimage = 48 ÷ (3/2) = 48 × (2/3) = 32 units.

Which scale factor did your problem give? (If it was 2/3, the preimage perimeter is 72 units; if 3/2, it is 32 units.)