To find the side length of a square when given the area, we need to take the square root of the area.
Given that the area of the square is 36w^2 + 60w + 25, we can factor the expression:
36w^2 + 60w + 25 = (6w + 5)^2
Now, taking the square root of both sides, we get:
√(36w^2 + 60w + 25) = √[(6w + 5)^2]
The square root of a perfect square on the right side simplifies to the expression within the parentheses:
√(36w^2 + 60w + 25) = 6w + 5
So, the side length of the square is 6w + 5.
Therefore, the correct answer is D. 6w + 5.