Alex has two different size bookends for his bigger books and smaller books. what is the length of the diagonal distance, x, of his smaller bookend? enter your answer, as a decimal, in the box.

The length of x is 7.2 in. The two triangles in the diagram are similar triangles. In other words, the lengths of their corresponding sides are proportional. In the first triangle, the ratio of the vertical length to the diagonal length is 10:12, and this proportionality is the same in the second triangle. 6:x=10:12, so x=6*12/10=7.2 in.