Ratio and Proportion - Scaling shapes up and down

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Scaling is the process of enlarging or reducing a shape while keeping its proportions the same.

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Scale Factor is the number used to multiply or divide all the side lengths of a shape.

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Enlargement occurs when the scale factor is greater than 1 (the shape gets bigger).

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Reduction occurs when the scale factor is less than 1 or when we divide by a whole number (the shape gets smaller).

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Corresponding Sides are sides that are in the same relative position in the original and the scaled shape.

📐Formulae

\text{New Length} = \text{Original Length} \times \text{Scale Factor}

\text{Original Length} = \text{New Length} \div \text{Scale Factor}

\text{Scale Factor} = \frac{\text{New Length}}{\text{Original Length}}

💡Examples

Problem 1:

A rectangle has a length of 5 cm and a width of 3 cm. If it is scaled up by a scale factor of 4, what are the new dimensions?

Solution:

5 \text{ cm} \times 4 = 20 \text{ cm}

Explanation:

To scale a shape up, multiply every original side length by the scale factor.

Problem 2:

A square with a side length of 12 cm is scaled down to a side length of 4 cm. What is the scale factor?

Solution:

\text{Scale Factor} = 12 \div 4 = 3

Explanation:

Compare the corresponding sides. Since the new side is 3 times smaller, the scale factor used to reduce it is 3.

Problem 3:

A triangle has a base of 10 cm. After being scaled, the new base is 25 cm. By what scale factor was the triangle enlarged?

Solution:

\text{Scale Factor} = 25 \div 10 = 2.5

Explanation:

25 / 10 = 2.5