Final answer:
To find the dimensions of the rectangle, set up a system of equations using the given information. Solve the system of equations using the substitution method. The dimensions of the rectangle are 19 meters by 8 meters.
Step-by-step explanation:
To find the dimensions of the rectangle, we'll start by assigning variables. Let L represent the length and W represent the width. Given that the difference between the length and width is 11 meters, we can set up the equation L - W = 11.
Additionally, we know that the perimeter of a rectangle is calculated as P = 2L + 2W. Since the perimeter is given as 54 meters, we can write the equation as 2L + 2W = 54.
1. Perimeter equation:
Perimeter = 2l + 2w = 54 meters
2. Difference equation:
l - w = 11 meters
Solving for l and w:
From equation 2, we can express l in terms of w: l = w + 11
Substitute this expression for l in equation 1:
2(w + 11) + 2w = 54
2w + 22 + 2w = 54
4w + 22 = 54
4w = 32
w = 8
Since l = w + 11, then:
l = 8 + 11 = 19
Therefore, the dimensions of the rectangle are 19 meters by 8 meters.