-The length of a rectangle is equal to triple the width.

Question

Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 86 centimeters?

Answer 1

Let's define the variables for the dimensions of the rectangle:

• Let \( w \) be the width of the rectangle.
• Let \( l \) be the length of the rectangle.

According to the problem, we have the following relationships:

1. The length is equal to triple the width: \[ l = 3w \]

2. The formula for the perimeter \( P \) of a rectangle is given by: \[ P = 2l + 2w \] In this problem, the perimeter is 86 centimeters, so: \[ 2l + 2w = 86 \]

Now, we can rewrite this system of equations:

1. \( l = 3w \) (Equation 1)
2. \( 2l + 2w = 86 \) (Equation 2)

Thus, the system of equations that can be used to find the dimensions of the rectangle is:

\[ \begin{align*}

1. & \quad l = 3w \
2. & \quad 2l + 2w = 86 \end{align*} \]