Final answer:
The correct system of equations to determine the dimensions of a rectangle with length three times the width and a perimeter of 86 centimeters is l = 3w and 2l + 2w = 86, which corresponds to option D.
Step-by-step explanation:
The question involves creating a system of equations to determine the dimensions of a rectangle, given that the length is thrice the width and the perimeter is 86 centimeters. To solve for the dimensions, we denote the width by w and the length by l. Using the information provided, we can construct two equations. The first equation represents the relationship between the length and the width: l = 3w.
The second equation is derived from the perimeter formula for a rectangle, which states that the perimeter P is equal to two times the length plus two times the width: P = 2l + 2w. Substituting the given perimeter value of 86 centimeters, we have 2l + 2w = 86. Therefore, the correct system of equations that can be used to find the dimensions of the rectangle is option D: l = 3w and 2l + 2w = 86.