Question

You have a 4x6 photo of you and your friend. You enlarge the original photo to three times its size on your computer. Is the new photo similar to the original?

Answer 1

Given a 4x6 photo, the aspect ratio of the photo is given by:

`\[\text{Aspect Ratio (Original)} = \frac{\text{Width (Original)}}{\text{Height (Original)}} = (4)/(6) = (2)/(3) = 0.6667\]`

Now, when the photo is enlarged to three times its size, the dimensions become
`\(12 * 18\)`. The aspect ratio for the enlarged photo is:

`\[\text{Aspect Ratio (Enlarged)} = \frac{\text{Width (Enlarged)}}{\text{Height (Enlarged)}} = (12)/(18) = (2)/(3) = 0.6667\]`

Since the aspect ratios of the original and enlarged photos are the same, the two photos are similar. In mathematical terms, two figures are considered similar if they have the same shape but may differ in size. Here, the shape (aspect ratio) of the photo remains consistent even after enlargement, so the enlarged photo is similar to the original.