Answer: Let's denote the length of the rectangular garden as L and the width as W.
We are given two pieces of information:
1. The perimeter of the rectangular garden plus the surrounding path is 30 meters.
2. The width of the garden is two-thirds its length.
To find the length and width, we can use these two pieces of information and solve the problem using algebraic equations.
Step 1: Express the perimeter in terms of L and W.
The perimeter of the rectangular garden is the sum of all four sides:
Perimeter = 2L + 2W
Step 2: Express the relationship between the width and length.
According to the given information, the width (W) is two-thirds of the length (L):
W = (2/3)L
Step 3: Substitute the width expression into the perimeter equation.
Substituting W = (2/3)L into the perimeter equation:
30 = 2L + 2(2/3)L
Step 4: Simplify and solve for L.
30 = 2L + (4/3)L
Multiplying the entire equation by 3 to eliminate the fraction:
90 = 6L + 4L
Combining like terms:
90 = 10L
Dividing both sides by 10:
L = 9
Step 5: Calculate the width using the relationship between L and W.
W = (2/3)L
W = (2/3)(9)
W = 6
Therefore, the length of the rectangular garden is 9 meters and the width is 6 meters.
Explanation: