Final answer:
To determine the width of a pond using a scale, we set up ratios to convert actual dimensions to scale dimensions. Using a scale of 1/2 inch to 5 feet for a 10 by 20 feet pond, we find the scaled width is 1 inch.
Step-by-step explanation:
Determine the Width of a Pond
To determine the width of a pond using a given scale, we employ the concept of ratios and proportions commonly used in mathematics. Mathematical scales are used to represent real-world dimensions in a smaller, more manageable size. The postulate or theorem used for such a scale conversion is not a single well-defined principle, but rather the fundamental concept of a ratio—which is a comparison of two quantities by division. To state a postulate or theorem, one would clearly and concisely articulate the rule or general principle it represents, supported by any necessary conditions or parameters.
For instance, in a problem where you need to convert measurements of a rectangular pond from actual size to scale size using a scale of 1/2 in = 5 ft, you would set up ratios to find the dimensions of the scale model. If the actual pond is 10 feet by 20 feet, the unit scale ratio would be 0.5 inches per 5 feet, written as:
- For the length: 0.5 inches/5 feet = L inches/20 feet
- For the width: 0.5 inches/5 feet = W inches/10 feet
By solving these proportions:
For the length, L = (0.5/5) × 20 = 2 inches,
For the width, W = (0.5/5) × 10 = 1 inch,
Therefore, the scale model of the pond should be 2 inches by 1 inch.