Final answer:
To find the length of the shorter side after enlarging a photograph with original dimensions of 6.5 inches by 5 inches to a longer side of 39 inches, we use proportional scaling. The scale factor is 39/6.5, which is 6. Therefore, the shorter side after enlargement is 30 inches.
Step-by-step explanation:
The problem is asking us to find the length of the shorter side of a photograph after enlargement. The original dimensions of the photograph are 6.5 inches by 5 inches. With the information given, the enlargement has made the longer side 39 inches. To solve this, we will use the concept of proportions because during enlargement, the aspect ratio of the photograph must remain the same.
Aspect ratio is the relationship of the width to the height and remains constant even when the image size changes. In this case, the enlargement keeps the original aspect ratio. Here's how we calculate the new dimensions:
- Original longer side: 6.5 inches
- Original shorter side: 5 inches
- New longer side: 39 inches
- Original aspect ratio (longer side to shorter side): 6.5/5
- Scale factor: 39 / 6.5 = 6
- New shorter side (using the scale factor): 5 inches * 6 = 30 inches
The shorter side after enlargement is 30 inches.