Question

The length of a rectangle is equal to triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 86 centimeters?

A. l=w+3 and 2l+2w=85
B. I=3w and 2l+2w=85
C. I= w³ and 2l+2w=85
D. I=3w+3 and 1l+2w=85

Answer 1

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:

1. l = 3w
2. 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.