KA-0155Scaling and similar figures
4 points, difficulty 2 of 3Level 7–8about 90sA photograph measures 8 cm by 12 cm. It is enlarged so that the shorter side becomes 20 cm, and the shape is not distorted. How long is the longer side of the enlargement?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
An enlargement multiplies both sides by the same number.
2The strategy
The shorter side went from 8 to 20. What number multiplies 8 to give 20?
3The full solution
20 / 8 = 2.5, so the longer side is 12 x 2.5 = 30 cm.
Solution
The reliable way
An enlargement multiplies every length by one scale factor. The shorter side went from 8 cm to 20 cm, so the factor is 20 / 8 = 2.5. Applying the same factor to the longer side gives 12 x 2.5 = 30 cm. Check the shape is preserved by comparing ratios: 8/12 = 20/30 = 2/3. The transferable idea: enlargements multiply, they do not add.
The elegant way
The sides are in the ratio 2 to 3, so a shorter side of 20 forces a longer side of 30.
Why this is on the test: Adding a constant instead of multiplying is the single most common scaling error, and it always distorts the shape.