Worked Example: Ratio and Proportion

1. Problem Statement

An engineering drawing is created with a scale of 1:50. If a structural column measures 85 mm on the drawing, what is its actual physical length in the real world?

2. Given Data

Drawing Length

85

mm

Scale Ratio

1 unit on drawing = 50 units in reality

1

: 50

3. Formula / Relationship

A scale ratio of $A:B$ means that a measurement $A$ on the drawing corresponds to a measurement $B$ in reality. $\frac{\text{Drawing Length}}{\text{Actual Length}} = \frac{1}{50}$

4. Substitution & Calculation

Let $L_{\text{actual}}$ be the actual length. We can set up the proportion: $\frac{85 \text{ mm}}{L_{\text{actual}}} = \frac{1}{50}$ Solving for $L_{\text{actual}}$ : $L_{\text{actual}} = 85 \text{ mm} \times 50 = 4250 \text{ mm}$

5. Final Result

Actual Length

4250

mm

6. Engineering Meaning

Ratios allow engineers to represent massive structures on small sheets of paper accurately. The proportion ensures that all dimensions scale uniformly, preserving the physical geometry. 4250 mm translates to 4.25 meters in reality.

Worked Example: Ratio and Proportion

Calculating Actual Length from a Scaled Drawing

1. Problem Statement

2. Given Data

3. Formula / Relationship

5. Final Result

6. Engineering Meaning

Calculating Actual Length from a Scaled Drawing

1. Problem Statement

2. Given Data

3. Formula / Relationship

4. Substitution & Calculation

5. Final Result

6. Engineering Meaning

4. Substitution & Calculation