Answer: stated down below
Explanation:
To determine the print sizes that Naomi can order without needing to crop the pictures or leave any extra space, we need to consider the aspect ratio of the pictures and the aspect ratios of the available print sizes.
The aspect ratio of the pictures is given as 3:2, which means that the width of the picture is 3/2 times the height. Let's denote the width as 3x and the height as 2x, where x is a positive constant.
Now, let's consider the available print sizes. Suppose the aspect ratio of a print size is given as a:b, where a represents the width and b represents the height. For the print size to accommodate the picture without any cropping or extra space, the aspect ratio of the print size must be equal to the aspect ratio of the picture.
We can set up a proportion using the aspect ratios of the picture and the print size:
(Width of Picture) / (Height of Picture) = (Width of Print Size) / (Height of Print Size)
Using the values we determined earlier:
(3x) / (2x) = a / b
Simplifying the equation:
3/2 = a / b
Cross-multiplying:
3b = 2a
This equation tells us that for the print size to match the aspect ratio of the picture without cropping or leaving extra space, the width of the print size (a) must be a multiple of 3, and the height of the print size (b) must be a multiple of 2.
Therefore, the print sizes that Naomi can order without needing to crop the pictures or leave any extra space are those that have aspect ratios that are multiples of the original aspect ratio of 3:2. For example, print sizes with aspect ratios of 6:4, 9:6, 12:8, and so on, would all be suitable without requiring any cropping or extra space.
By considering the properties of similar figures and setting up the proportion using the aspect ratios, we can determine which print sizes will preserve the entire picture without any cropping or additional space on the sides.