Look at it this way: you have a rectangular block with length = a, width = b and height = c. What you need to do is prove that a = b = c.

Now, you start with the fact that its base is 60, meaning that ab = 60.

1. tells you that the front face is also 60, meaning that ac = 60 as well. So you have that:
ac = 60
ab = 60

The only extra info you have is that c = b, but we don't know if a is or is not equal to the the two. For all we know, b = c = 12 and a = 5. So 1 isn't enough.

2. basically is the same as 1, just with a bit of variation: here you have that bc = ab = 60, meaning that a = c. Again, it's not enough since you need to have a relationship between all three sides.

But put the two together and you get that:
b = c
a = c

This means that, in the end, a = b = c, making the rectangular block a cube. So C is indeed the answer.

thanks a lot, DanaJ. ur explanation is more lucid than the official one