Help with polynomial equations?

I've been trying to solve these. I've drawn a picture, and that doesn't help either. I just don't know how to solve word problems like these. Thank you.



Landscaping. A rectangular lawn measures 60 ft by 80 ft. Part of the lawn is torn up to install a sidewalk of uniform width around it. The area of the new garden is one-half the area of the old garden. How wide is the walkway?



Tent design. The triangular entrance to a tent is 2 ft taller than it is wide. The area of the entrance is 12 ft^2. Find the height and the base.



Sailing. A triangular sail is 9 m taller than it is wide. The area is 56 m^2. Find the height and the base of the sail.

Help with polynomial equations?
You can write 3 equations for the first problem: let x = width of sidewalk. If you sketch your new garden inside the old, you see that in the long direction, the length , 80, is x + y + x

In the short direction, you have x + x + z = 60.



You also know that y * z, the dimesions of the new garden = 2400



So, simplify: If 2x + y = 80 and 2x + z = 60, we find that y - z = -20

We substitute y = 2400/z into the y - z = -20 equation

Simplifying, we get y = 60 ft and then substituting into y * z = 2400 we find that z = 40 ft



Next, go back to either of the two equations that describe the length: 2x + y = 80. Since we know that y = 60, we solve for x and find that x = 10 ft



The tent problem:



Height = base + 2

A = 1/2 (h * b)

12ft^2 =(1/2) (b + 2)b

24 = b^2 + 2b

b = 4

h = 6



Sail problem is the same as the tent:

h = b + 9



56 = (1/2)(b+9)b

b = 7

h = 16
Reply:the first one is 17 1/2 ft. wide. gimme a sec. I'm working on the second and third ones.