Question

The square below is dilated by a scale factor of 4. Find the perimeter and area of the square below, as well as the perimeter and area of the dilated square. Express your answers as whole numbers, decimals, or fractions in simplest terms (no mixed numbers). Figures are not necessarily drawn to scale. The number for the small triangle is 3. Perimeter of given square_ units. Perimeter of dilated square _ units. Area of given square _ units^2. Area of dilated square _ units^2.

Answer 1

I don't have the figure, so I need one clarification: does the "3" label mean the side length of the given square is 3 units? If not, what does the 3 refer to in the picture?

If the square's side length s = 3, then:
- Perimeter of given square = 4s = 4(3) = 12 units.
- Under a dilation of scale factor 4 the new side = 4s = 12, so perimeter of dilated square = 4(12) = 48 units.
- Area of given square = s^2 = 3^2 = 9 units^2.
- Area of dilated square = (4s)^2 = 16s^2 = 16(9) = 144 units^2.

So (for s = 3): Perimeter original = 12 units, Perimeter dilated = 48 units, Area original = 9 units^2, Area dilated = 144 units^2.

If the "3" in the picture means something else, please upload the figure or explain what segment it labels and I will recompute.