KJSEA 2025 Maths Q16 — Scale Drawing (1:100)

KJSEA 2025 Grade 9 Measurement

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The Question

“An architectural drawing uses a scale of 1 to 100. A wall built from this drawing is 3 metres long in real life. What was the length of the wall on the drawing?”

1

Understand the scale

A scale of 1 to 100 means that every 1 centimetre measured on the paper represents 100 centimetres on the actual building. Both numbers in the scale must be thought of in the same unit, so here we work in centimetres.

1:100⇒1 cm on paper=100 cm in real life1 : 100 \Rightarrow 1\text{ cm on paper} = 100\text{ cm in real life}
2

Convert the real length to centimetres

The scale compares centimetres to centimetres, but the wall is given in metres. To use the scale we first change the real length into centimetres, because one metre is one hundred centimetres.

3 m=3×100=300 cm3\text{ m} = 3 \times 100 = 300\text{ cm}
3

Divide the real length by the scale factor

The drawing is smaller than the real wall by a factor of 100, so to go from the real length back to the drawing length we divide by 100.

drawing length=300100=3 cm\text{drawing length} = \frac{300}{100} = 3\text{ cm}

Final Result

On the drawing, the wall was 3 cm long. This is option B.

Why this method works

A scale is a fixed ratio between the drawing and reality. Because 1:100 means every real distance is 100 times bigger than its picture, the reverse move — from reality to the drawing — must shrink the length by the same factor of 100. Dividing 300 cm by 100 undoes the enlargement and gives the true length on the paper, but only after both quantities share the same unit, which is why converting metres to centimetres comes first.

✓

Reverse it: 3 cm on the drawing times 100 gives 300 cm, which is 3 m, matching the real wall.