A rectangular red sticker has an area of 108 square millimetres and a perimeter of 42 millimetres. What are the dimensions of the sticker?

The dimensions of the rectangle can be found by solving the system of equations derived from the given area and perimeter.

The area (A) of a rectangle is given by the formula A = length * width. So, we have:

108 = length * width ----(equation 1)

The perimeter (P) of a rectangle is given by the formula P = 2 * (length + width). So, we have:

42 = 2 * (length + width) ----(equation 2)

Solving equation 2 for length, we get:

length = 21 - width

Substitute this into equation 1, we get:

108 = (21 - width) * width

Solving this quadratic equation, we get two possible solutions for width: 12 mm and 9 mm.

Substituting these values back into the equation for length, we get two possible solutions for length: 9 mm and 12 mm.

So, the dimensions of the sticker are 12 mm by 9 mm.