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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?

1 answer

To find the dimensions of the rectangle, we can set up a system of equations based on the information provided.

Let:

  • \( w \) = width of the rectangle
  • \( l \) = length of the rectangle

From the problem, we know two things:

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

  2. The perimeter of the rectangle is 86 centimeters. The formula for the perimeter \( P \) of a rectangle is given by: \[ P = 2l + 2w \] Plugging in the perimeter: \[ 2l + 2w = 86 \]

Now we can substitute \( l \) from the first equation into the second equation: \[ 2(3w) + 2w = 86 \] This simplifies to: \[ 6w + 2w = 86 \] or: \[ 8w = 86 \]

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

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

This is the correct system to find the dimensions of the rectangle.