Scale Drawing - GCSE Maths - Steps, Examples & Worksheet - Free Printable

Problem Analysis:

The image describes a scale drawing of a pool with a given scale factor. The task involves understanding how the scale factor is applied to convert measurements between the scale drawing and the real object.

#### Key Information Provided:
1. Scale Factor: The scale is given as \( 1 \text{ cm} : 2 \text{ m} \) or equivalently \( 1:200 \). This means:
- Every 1 cm in the scale drawing represents 2 meters in real life.
- The scale factor for enlargement is \( \frac{1}{200} \), meaning the real object is 200 times larger than its representation in the scale drawing.

2. Example Measurement:
- In the scale drawing, the length of the pool is 6 cm.
- In real life, the corresponding length of the pool is 12 meters.

#### Objective:
We need to understand how the scale factor is used to convert measurements between the scale drawing and the real object. Specifically:
- How do we calculate the real-life dimensions from the scale drawing?
- How do we calculate the scale drawing dimensions from the real-life dimensions?

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Solution Explanation:

#### Step 1: Understanding the Scale Factor
The scale factor \( 1:200 \) tells us that:
- To find the real-life measurement from the scale drawing, we multiply the scale drawing measurement by 200.
- To find the scale drawing measurement from the real-life measurement, we divide the real-life measurement by 200.

#### Step 2: Converting from Scale Drawing to Real Life
If a measurement in the scale drawing is \( x \) cm, the corresponding real-life measurement in meters is calculated as:
\[
\text{Real-life measurement (in meters)} = x \times 2
\]
This is because \( 1 \text{ cm} \) in the scale drawing represents \( 2 \text{ m} \) in real life.

Alternatively, using the scale factor \( 1:200 \):
\[
\text{Real-life measurement (in meters)} = x \times 200 \quad \text{(if converting directly to meters)}
\]

#### Step 3: Converting from Real Life to Scale Drawing
If a measurement in real life is \( y \) meters, the corresponding scale drawing measurement in cm is calculated as:
\[
\text{Scale drawing measurement (in cm)} = \frac{y}{2}
\]
This is because \( 2 \text{ m} \) in real life corresponds to \( 1 \text{ cm} \) in the scale drawing.

Alternatively, using the scale factor \( 1:200 \):
\[
\text{Scale drawing measurement (in cm)} = \frac{y \times 100}{200} = \frac{y}{2}
\]
(Note: We multiply by 100 to convert meters to centimeters before applying the scale factor.)

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Example Calculations:

1. From Scale Drawing to Real Life:
- Scale drawing length = 6 cm
- Real-life length = \( 6 \times 2 = 12 \) meters (or \( 6 \times 200 = 1200 \) cm = 12 meters).

2. From Real Life to Scale Drawing:
- Real-life length = 12 meters
- Scale drawing length = \( \frac{12}{2} = 6 \) cm (or \( \frac{12 \times 100}{200} = 6 \) cm).

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Final Answer:

The scale factor \( 1:200 \) is used to convert measurements as follows:
- To find the real-life measurement: Multiply the scale drawing measurement by 200.
- To find the scale drawing measurement: Divide the real-life measurement by 200.

\[
\boxed{1:200}
\]