Final answer:
To enlarge a picture with original dimensions of 3 inches by 5 inches to a width of 2 feet, convert the desired width to inches, determine the scale factor, and multiply the original height by this scale factor to find the required height for the enlarged picture, which is 14.4 inches.
Step-by-step explanation:
The student has asked how tall an enlarged picture will need to be if it was originally 3 inches tall and 5 inches wide and is to be enlarged to be 2 feet wide. To solve this problem, we need to use the concept of scale factors to maintain the same aspect ratio of the original picture.
First, convert the width of the enlarged picture to inches because the original dimensions are in inches. There are 12 inches in a foot, so 2 feet is 24 inches. Now, calculate the scale factor by dividing the width of the enlarged picture by the width of the original picture. The scale factor is 24 inches / 5 inches = 4.8.
Now, multiply the original height by the scale factor to find the height of the enlarged picture. 3 inches × 4.8 = 14.4 inches. Therefore, the height of the enlarged picture will need to be 14.4 inches to maintain the same aspect ratio.