What are the dimensions of the book?

Question

There are five copies of a book each 20mm thick. When tilted, they fit snugly inside a cubic box with a gap of 16mm at the bottom left as shown.

I struggled with this in a recent practice paper, any help appreciated.

Answer 1

Hint

The triangles are all similar to one another, all of them to the (12,16,20) right angles triangle. So, assuming cubic box of side $a$, we have the triangle (12,16,20) is similar to the triangle ($a-80$, $a-12$, $l$) formed by the book's surface and two perpendicular edges

Hence

$$\frac{a-80}{a-12} = \frac{3}{4}$$

That will give you $a$ as well as the book dimensions