For this problem, it would suffice to find the length of any side then multiply it by 4, since they are all equal. To find that, it would be very easy if ABE is a right triangle. Since we're given the side lengths of AE and BE, we actually can say that it is a right angle.
That's because
So, since the sum of each leg squared equals the hypotenuse squared, this triangle is right. It's a corollary of pythaogreans.
Now we know that AB has a length of 15, so the perimeter is 60 since they're all equal.