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?

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:

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