Question

The rectangle below is dilated by a scale factor of 4. 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. Perimeter of given rectangle _ units. Perimeter of dilated rectangle _ units. Area of given rectangle _ units^2. Area of dilated rectangle _
units^2.

Answer 1

I can’t see the rectangle — could you tell me the side lengths (or upload the picture)?

In the meantime here are the formulas and the quick scaling facts you’ll need (scale factor k = 4):

- If the original rectangle has length L and width W:
- Perimeter P = 2(L + W)
- Area A = L × W
- After a dilation by k = 4:
- New side lengths = 4L and 4W
- New perimeter P' = 2(4L + 4W) = 4 · 2(L + W) = 4P
- New area A' = (4L)(4W) = 16 · (L W) = 16A

So once you give L and W I will compute:
- Perimeter of given rectangle = 2(L + W) units
- Perimeter of dilated rectangle = 4 · 2(L + W) = 8(L + W) units
- Area of given rectangle = L·W units^2
- Area of dilated rectangle = 16·L·W units^2

Example: if L = 6 and W = 2 then
- P = 2(6 + 2) = 16 units
- P' = 4·16 = 64 units
- A = 6·2 = 12 units^2
- A' = 16·12 = 192 units^2

Give the rectangle’s side lengths and I’ll compute the exact answers.