You are right to start with L*W = 60. Now, think about L and W for a second: they're lengths of sides, so they must be positive. With that in mind we can go on to analyze the stmts:

1. the key word here is "integers": there are plenty of numbers that, when multiplied, yield 60. For instance, 2/3 and 90 and a lot of other fractions. But there are only a few integers that follow this rule and even fewer even integers that are smaller than 25.
In order to zoom in on these particular integers, just use the prime factorization of 60 = 2^2*3*5.
Now, we know we're dealing with even integers, so both L and W get a 2 respectively. Now, after splitting the 2s, you need to figure out what you're going to do with 3 and 5. Say you choose to have L = 2*3*5 (meaning you put both 3 and 5 in the same place) and W = 2. But this means that L = 30, which is greater than 25. This is why you need to have L = 2*3 and W = 2*5 or L = 2*5 and W = 2*3.

In any case, you have that L + w = 6 + 10 = 16. Since the perimeter is 2(L + W), it will be 32. So 1 is sufficient.

2. L > 3W doesn't help much. Consider some cases:
a. L = 60 and W = 1
b. L = 90 and W = 2/3.
Since there is no single solution, 2 is insufficient.