Proportion and scaling models

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Formula

Explanation

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Worked solution

1. The scale model of the escalator has a vertical rise of 0.8 m and a horizontal run of 1.5 m. These are the legs of a right-angled triangle, with the escalator as the hypotenuse.
2. Use the Pythagorean theorem: c² = a² + b², where c is the hypotenuse (actual escalator length), a is the vertical rise, and b is the horizontal run.
3. Substitute the model's dimensions into the formula: c² = (0.8)² + (1.5)².
4. Calculate (0.8)² = 0.64 and (1.5)² = 2.25.
5. Add the squares: 0.64 + 2.25 = 2.89.
6. Take the square root of 2.89 to find c: c = sqrt(2.89).
7. sqrt(2.89) = 1.7, since 1.7 × 1.7 = 2.89.
8. The model escalator length is 1.7 m. This is at a scale of 1:25, meaning 1 unit on the model equals 25 units in real life.
9. Multiply the model length by 25 to find the actual length: 1.7 × 25.
10. Calculate 1.7 × 25 = 42.5.
11. The actual escalator length is 42.5 metres.
12. Check: 42.5 ÷ 25 = 1.7, which matches the model length. The calculation is consistent.

Reference answer: 42.5

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