Final answer:
The enlarged picture, which is 10 feet long, will be 6.67 feet wide after maintaining the original aspect ratio and converting all measurements into a consistent unit (inches), then solving the proportion.
Step-by-step explanation:
To find the width of the picture when it is enlarged, we will use a proportion based on the relationship between the original dimensions and the enlarged dimensions. The original picture has a width of 4 inches and a length of 6 inches. It is enlarged to a length of 10 feet, and we need to find the new width while maintaining the same aspect ratio.
First, convert the length from feet to inches to align units:
- 10 feet = 10 x 12 inches = 120 inches
Now, set up a proportion using the original and enlarged lengths:
Original length/Enlarged length = Original width/Enlarged width
6 inches/120 inches = 4 inches/w inches
Now cross-multiply and solve for the unknown width (w):
6w = 4 x 120
w = (4 x 120)/6
w = 480/6
w = 80 inches
Finally, convert inches back to feet:
80 inches / 12 inches per foot = 6.67 feet.
Therefore, the width of the enlarged picture will be 6.67 feet, which corresponds to Option A.