2026 ACJC P1 Q3

A piece of cardboard has the shape of an equilateral triangle, with fixed side length \(l\) cm. Six perpendicular cuts, each of length \(x\) cm, are made to the cardboard to remove the corners. The remaining cardboard is then folded to form an open box with an equilateral triangular base.

1. Show that the length of the equilateral triangular base is \(l-2x\sqrt3\).[1]
2. Find the value of \(x\), in terms of \(l\), that gives the maximum volume of the open box. (You need not show that your answer gives a maximum.)[3]