Final answer:
By setting up a proportion based on the width-to-length ratio (10w to 19l), where the width is 40 inches, the corresponding length is calculated to be 76 inches.
Step-by-step explanation:
The question asks us to find the length of a flag given its width and the ratio of width to length. With a flag width of 40 inches and a ratio of 10w to 19l (width to length), where 'w' and 'l' represent the width and length in units, respectively, we can set up a proportion to solve for the length of the flag.
Using the ratio 10 : 19l, we can say that 10 inches of width corresponds to 19 inches of length. When the actual width (w) is 40 inches, we can set up the proportion as:
10w / 19l = 40 inches / x inches
Substituting the value of w:
10 * 40 / 19 = 40 / x
By cross-multiplying, we get:
10 * 40 * x = 19 * 40
x = (19 * 40) / (10 * 40)
x = 19/10
x = 76 inches
Therefore, the correct length of the flag is 76 inches.