Final answer:
To find the width of the large rectangle with the same ratio as the small rectangle, we set up a proportion based on their lengths and widths which results in 9/8 = 24/w. Solving for w gives us 21.33 inches as the width of the large rectangle.
Step-by-step explanation:
The width of the large rectangle can be determined by using the ratio of the lengths and widths of the rectangles. Since the length of a small rectangle is 9 in and the width is 8 in, the ratio of length to width for the small rectangle is 9:8. Given that the ratio remains the same for the large rectangle, and its length is 24 in, we can set up a proportion to find its width.
Let w be the width of the large rectangle. The proportion based on the ratios is:
\(\frac{9}{8} = \frac{24}{w}\)
Now, cross-multiply to solve for w:
8 \(\times\) 24 = 9 \(\times\) w
192 = 9w
w = \(\frac{192}{9}\)
w = 21.33 in
Therefore, the width of the large rectangle is 21.33 inches, maintaining the same length-to-width ratio as the small rectangle.