A wire, 12 metres long, is cut into two pieces - NSC Mathematics - Question 9 - 2023 - Paper 1

Let the length of a side of the equilateral triangle be $2x$. The perimeter of the triangle is then given by:

$3(2x) = 6x.$
The total length of the wire is 12 metres. Thus, the length used for the square is:

$12 - 6x.$
Since a square has four equal sides, the length of one side of the square, denoted as $b$, can be derived from:

$4b = 12 - 6x.$
Rearranging gives:

$b = \frac{12 - 6x}{4} = 3 - \frac{3x}{2}.$
Therefore, the length of a side of the square in terms of $x$ is:

$b = 3 - \frac{3x}{2}.$