It will be roughly 67.08 inches.
We can solve this using the Pythagorean Theorem, which is listed below.
[tex] a^{2} + b^{2} = c^{2} [/tex]
In this equation, we use a and b as legs of a triangle and c is the hypotenuse. We can treat the length and height of the bookcase as legs and use this equation to solve for the diagonal (also known as the hypotenuse)
[tex] 30^{2} + 60^{2} = c^{2} [/tex]
[tex] 900 + 3600 = c^{2} [/tex]
[tex] 4500 = c^{2} [/tex]
67.08 = c
