A graphic designer in a newspaper editorial received two images to place next to an article. The first original was $13 \mathrm{~cm}$ wide and $9 \mathrm{~cm}$ tall, the second measured $14 \mathrm{~cm}$ in width and $12 \mathrm{~cm}$ in height. The graphic designer decided to place the images on the page side by side so that they touch and both have the same height. After printing, the images together should occupy a width of $18.8 \mathrm{~cm}$. Therefore, he appropriately reduced the size of the images without cropping them in any way.

What will be the height of the printed images?
First, we reduce the second image so that it has the same height as the first, and then we resize both so that together they have the given width:

To make the second image have the same height as the first, we need to reduce it in the ratio $\frac{9}{12}=\frac{3}{4}$. The width of this reduced image will then be $\frac{3}{4} \cdot 14=10.5(\mathrm{~cm})$. Now, the first image and the reduced second image, placed side by side, form a rectangle with dimensions $23.5 \mathrm{~cm} \times 9 \mathrm{~cm}$. We will then resize this whole to make the width equal to the given $18.8 \mathrm{~cm}$. We will reduce it in the ratio $\frac{18.8}{23.5}=\frac{4}{5}$, and the height of the whole will then be $\frac{4}{5} \cdot 9=7.2(\mathrm{~cm})$.