The larger square garden at Volterra Hall has sides twice as long as the smaller square garden. Together the gardens cover 18,000 square feet. Find the dimensions of each garden.

Comment
The gardens are square. There are two of them. The total is 18000 square feet. There is a relationship between smallest and largest square.

Development of the Equation.
Formula for a square = s*s

The first garden has a side of s
The larger garden has a side of 2s

The area of the first garden = s^2
The area of the 2nd garden = (2s)^2

The two areas together are
s^2 + (2s)^2 = 18000

Solve
s^2 + 4s^2 = 18000 Add the like terms on the left.
5s^2 = 18000 Divide by 5
s^2 = 18000/5
s^2 = 3600 Take the square root of both sides.
sqrt(s^2) = sqrt(3600)
s = 60 For the small garden

2s = 2*s = 2*60 = 120 for the large garden.

Answers
Small garden = 60 by 60
Large garden = 120 by 120

Check 
Area of the small garden = 60 * 60 = 3600
Area of the large garden = 120*120 = 14400
Total Area = 18000 and it checks.