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Core Scale Factors

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Core Scale factors

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Part 1: Calculate the Scale Factors

Multiply every corresponding length by the same positive scale factor. Show your working.

1. A rectangle has side lengths 6 cm and 4 cm. It is enlarged by a scale factor of 2. Find the new side lengths.
2. A triangle has side lengths 9 cm, 6 cm and 3 cm. It is reduced by a scale factor of 1/3. Find the new side lengths.
3. A rectangle has side lengths 10 m and 7 m. It is reduced by a scale factor of 1/2. Find the new side lengths.
4. A triangle has side lengths 8 cm, 5 cm and 4 cm. It is enlarged by a scale factor of 1.5. Find the new side lengths.
5. A length of 5 cm becomes 15 cm. What is the scale factor? Does this enlarge or reduce the shape?
6. A rectangle is enlarged by a scale factor greater than 1. Which statement is correct?

Every corresponding length becomes shorter.

Every corresponding length becomes longer.

The angles change but the lengths stay the same.

Part 2: Check and Draw

7. A triangle has original side lengths 4 cm, 5 cm and 6 cm. A response gives new side lengths of 8 cm, 5 cm and 12 cm. Identify the error and explain why the response is flawed.
8. Draw a rectangle measuring 4 cm by 2.5 cm. Enlarge it using a scale factor of 1.5. Label the new lengths.
9. Measure your enlarged rectangle. Check the matching ratios using the original and new lengths. Complete the statements:

New length ÷ original length = ________

New width ÷ original width = ________

Are the ratios matching? ______________________________

10. What happens to the angles when a shape is enlarged or reduced?

Answer Key

1. 12 cm and 8 cm.

2. 3 cm, 2 cm and 1 cm.

3. 5 m and 3.5 m.

4. 12 cm, 7.5 cm and 6 cm.

5. Scale factor 3; it enlarges the shape.

6. Every corresponding length becomes longer.

7. The 5 cm side was not scaled. The matching ratios are not all the same: 8 ÷ 4 = 2, 5 ÷ 5 = 1 and 12 ÷ 6 = 2.

8. New rectangle: 6 cm by 3.75 cm.

9. Both ratios should be 1.5, so they match.

10. The angles remain unchanged.

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