Final answer:
To find the dimensions of the rectangle, we need to set up and solve a system of equations using the given information. The dimensions of the rectangle are w = 10 and l = 48.
Step-by-step explanation:
Let's denote the width of the rectangle as w and the length as l.
From the given information, we can set up two relationships:
The perimeter of a rectangle is given by: P = 2w + 2l
The length is 18 more than 3 times the width: l = 3w + 18
To find the dimensions, we need to solve these two equations simultaneously to find the values of w and l.
Substituting the second equation into the perimeter formula, we get: 2w + 2(3w + 18) = 116
Simplifying this equation gives us: 8w + 36 = 116
Next, we can solve for w: 8w = 80
Finally, we can find the value of l by substituting the value of w back into the second equation: l = 3(10) + 18
Therefore, the dimensions of the rectangle are w = 10 and l = 48.