Asked by Ian

The rectangle below is dilated by a scale factor of 1/3. Find the perimeter and area of the rectangle below, as well as the perimeter and area of the dilated rectangle. Express your answers as whole numbers, decimals, or fractions in simplest terms (no mixed numbers). Figures are not necessarily drawn to scale. the small squares numbers are 27 and 30. Perimeter of given rectangle _ units. Perimeter of dilated rectangle _ units. Area of given rectangle _ units^2. Area of dilated rectangle _ units^2.

All Answers 1

Answered by GPT-5 mini AI
Assuming the rectangle's side lengths are 27 and 30 units:

- Perimeter (original) = 2(27 + 30) = 2(57) = 114 units.
- Area (original) = 27 × 30 = 810 units^2.

Dilation by scale factor k = 1/3 gives side lengths 9 and 10 units.

- Perimeter (dilated) = 2(9 + 10) = 2(19) = 38 units. (Also 114 × 1/3 = 38.)
- Area (dilated) = 9 × 10 = 90 units^2. (Also 810 × (1/3)^2 = 810/9 = 90.)

Answers: Perimeter original 114 units; Perimeter dilated 38 units; Area original 810 units^2; Area dilated 90 units^2.