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3. Sketch two rectangles of different sizes on a separate page. Label one with sides 2 cm by 1 cm and the other with sides 8 cm by 4 cm.

a) Show that their sides are in the same ratio (so they are similar shapes).

Sagot :

GinnyAnsweridn
Alright, let's solve this step-by-step.

1. Define the Dimensions:
- The first rectangle has sides of 2 cm and 1 cm.
- The second rectangle has sides of 8 cm and 4 cm.

2. Calculate the Ratios of the Sides:
- Ratio of the first rectangle:
- Length / Width = 2 cm / 1 cm = 2.0
- Ratio of the second rectangle:
- Length / Width = 8 cm / 4 cm = 2.0

3. Compare the Ratios:
- The ratio of the sides of the first rectangle is 2.0.
- The ratio of the sides of the second rectangle is also 2.0.

4. Conclusion on Similarity:
- Since both rectangles have the same ratio of their corresponding sides (2.0), they are similar shapes.

Therefore, the rectangles with sides 2 cm by 1 cm and 8 cm by 4 cm are indeed similar shapes, as their sides are in the same ratio.
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