Find the perimeter of the preimage, the original rectangle, before its dilation.

Question

The rectangle below is the image of a rectangle that was dilated by a scale factor of 3. Find the perimeter of the preimage, the original rectangle, before its dilation. Figures are not necessarily drawn to scale.

9

_____________

| |

| |

| | 15

| |

| |

|_____________|

Answer 1

Since the original rectangle was dilated by a factor of 3, the original rectangle was 1/3 the dimensions of the dilated rectangle and thus its perimeter is 1/3 the perimeter of the dilated rectangle.

The perimeter of the dilated rectangle is 9 * 2 + 15 *2 = 48.

so the perimeter of the original rectangle is 48/3 = 16.