[10.02] a square with a side of 12 is increased to a side of 15. by how much is the diagonal increased?

A square with side = 12 will have diagonal (use Pythagoras' Theorem)
12^2 + 12^2 = disgonal^2
diagonal^2 = 288
diagonal = 16.9705627485

With side = 15
15^2 + 15^2 = 450
diagonal = 21.2132034356

So the diagonal increases by a factor of
21.2132034356 / 16.9705627485
An increase by a factor of 1.25 exactly