Final answer:
Measurements that fit the Pythagorean theorem can represent the side lengths of a right triangle. For instance, side lengths of 9 feet and 5 feet would result in a hypotenuse of approximately 10.3 feet. When writing proportions, it's crucial to keep the units the same for accurate comparisons.
Step-by-step explanation:
To determine which measurements could represent the side lengths in feet of a right triangle, we can utilize the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Using the formula c = √a² + b², where 'c' represents the length of the hypotenuse and 'a' and 'b' represent the lengths of the other two sides, we can calculate the possible measurements. For example, consider a right triangle with side lengths of 9 feet and 5 feet. We can determine the length of the hypotenuse by calculating √(9 feet)² + (5 feet)², which equals √81 + 25, or √106 feet, which is approximately 10.3 feet when rounded to three significant figures.
Additionally, when writing proportions to relate scale distances to actual distances, keeping units consistent is essential. For instance, if the scale measurement in inches is provided for a building and you need to compare it to the actual size in feet, you will have to convert inches to feet or vice versa before setting up the ratios.