Charlie has an 8m plank. He plans to cut it into 4 pieces to make a rectangular sandbox. Show that he can maximize the area of the sandbox by using a square

Question

I don't know what to do here ??? please help

 

Continuation to question- with a side length of 2m

Answer 1

Asaume that rectangle's dimensions are L and W and that 2L+2W = 8.

solve for L in terms of W.

Area = LW becomes f(W), a quadratic function.

The function takes on its maximum at the vertex (because leading coefficient is negative). This allows you to find W and thus L. They'll be equal (each is 2) and that's a square, as is always the case in this type of "max. area of rectangle" problem.