A rectangular garden is 30 m long and 20 m wide. A path of uniform width is set around the edge that reduces its area to 375m^2. What is the width of the path?
To find the width of the path, we can use the concept of area to solve this problem.
Step 1: Let's start by calculating the original area of the rectangular garden before the path was added.
The original length of the garden is given as 30m, and the width is given as 20m. To find the area, we multiply the length by the width:
Area of the rectangular garden = length x width
= 30m x 20m
= 600m^2
Step 2: Now, we need to find the area of the garden with the path included. The problem states that this area is 375m^2.
Area of the garden with path = 375m^2
Step 3: The area taken up by the path can be found by subtracting the original area of the garden from the area of the garden with the path:
Area of the path = Area of the garden without path - Area of the garden with path
Let's denote the width of the path as 'x'.
Area of the garden without path = (30 - 2x) x (20 - 2x)
Area of the path = (30 - 2x) x (20 - 2x) - 600m^2
Step 4: Finally, we can equate the area taken up by the path to 375m^2 and solve for 'x'.
(30 - 2x) x (20 - 2x) - 600m^2 = 375m^2
After solving this equation, we will get the value of 'x', which represents the width of the path.