EXPLANATION
Let's see the facts:
Sophia's garden shape: rectangular
The perimeter of the garden = 80 ft (conditional)
Length = 10+2Width ---> l = 10+2w (conditional)
As we can see, there are two variables and two equations, so we must solve this system of equations:
(1) p = 2 (w+l) = 80 (Perimeter Formula)
(2) l = 10 + 2w (Conditional)
Now, we can solve (1) equation and replace in (2):
80 = 2w + 2l (Isolating w)
80 - 2l = 2w (Dividing both sides by 2)
40 - l = w
Now, replacing in (2):
l = 10 + 2(40-l) (Applying distributive property)
l = 10 + 80 - 2l (Adding +2l to both sides and simplifying)
3l = 90 (Dividing both sides by 3)
l = 30
Now, we have l=30, so with this variable can calculate w in this way:
w = 40 - l = 40 - 30 = 10
w = 10
Now we have the dimensions: Width=10ft and Length= 30ft
[ANSWER] The dimensions are: Width=10 feet and Length= 30 feet