Final answer:
The question asks for a correct system of equations to find the dimensions of a rectangle with a known relationship between length and width, and a given perimeter. The correct option is B: l=3w and 2l+2w=86, allowing for the calculations of the rectangle's length and width.
Step-by-step explanation:
The student is asking for a system of equations that can be used to find the dimensions of a rectangle given that the length is equal to triple the width and that the perimeter is 86 centimeters. To find the dimensions of the rectangle, we can use two equations: one that relates the length and width, and another that represents the perimeter of the rectangle.
Let's denote the width of the rectangle as w and the length as l. According to the problem, the length is triple the width, which is mathematically represented as l = 3w. Now, the perimeter P of a rectangle is given by the formula P = 2l + 2w, and we know the perimeter is 86 centimeters, so we have 2l + 2w = 86.
Using these two equations, we can create a system of equations:
- l = 3w
- 2l + 2w = 86
The correct option that represents this system is option B: l=3w and 2l+2w=86. This system of equations will allow us to solve for both the length and the width of the rectangle.