Question

Rectangle A has a length of 6 cm and a width of 3 cm. Rectangle B has a length of 18 cm and a width of 6 cm. Rectangle C has a length of 18 cm and a width of 9 cm Is Rectangle C a scaled copy of Rectangle A?

Answer 1

To determine whether Rectangle C is a scaled copy of Rectangle A, we need to compare their dimensions and check if the length-to-width ratio (aspect ratio) is the same for both rectangles.

First, let's calculate the aspect ratio for both rectangles:

- **Rectangle A**:
- Length: 6 cm
- Width: 3 cm
- Aspect Ratio of A = Length / Width = 6 cm / 3 cm = 2

- **Rectangle C**:
- Length: 18 cm
- Width: 9 cm
- Aspect Ratio of C = Length / Width = 18 cm / 9 cm = 2

Since both rectangles have the same aspect ratio of 2, we confirm that Rectangle C is a scaled copy of Rectangle A.

To further check, see if the lengths and widths of the rectangles maintain the same ratio. We can find the scale factor:

- Scale Factor from A to C:
- Length: \( \frac{18\, \text{cm}}{6\, \text{cm}} = 3 \)
- Width: \( \frac{9\, \text{cm}}{3\, \text{cm}} = 3 \)

Since both ratios equal the same scale factor of 3, Rectangle C is indeed a scaled copy of Rectangle A.