Final answer:
To determine 'w', the width of a rectangle with the same height-to-width ratio as a given proportion, we set up a proportion comparing the known and unknown measurements. Using cross-multiplication, we solve for 'w'. The consistent use of units throughout the calculation is essential for accuracy.
Step-by-step explanation:
To find the value of w when the rectangles have the same height-to-width ratio, we employ proportions. A proportion expresses the relationship between two ratios or fractions. In this context, we will be comparing the scale of a drawing or model to the actual dimensions of the object it represents. By setting the two height-to-width ratios equal to one another, we ultimately solve for the unknown variable w.
As an example, if the proportion is given by scale/actual equals 1/50, and we have length ratios such as 0.5 on a scale drawing to 5 feet in reality, we set up the equation 1/50 = 0.5/5 to solve for the actual length. Similarly, for width, if our scale/actual ratio is w/10 equals 0.5/5, we use cross-multiplication to solve for w. In this specific case, there is a given example of the proportion 1/48 equals w/16. By cross-multiplying (1 times 16 = 48 times w), we can find that w equals 100 feet.
It's crucial to maintain consistency in units when working with proportions. If the proportion involves feet, we keep all measurements in feet to solve for w.