Question 269127
The volume of the open-top box (V) is given as 300 sq.ft.
For a rectangular prism (a box), the volume is given by:
{{{V = L*W*h}}} and, in this problem, V = 300 sq.ft., h = 4 ft., W = W and L = 3W, so...
{{{(3W)*(W)*4 = 300}}} Simplify.
{{{12W^2 = 300}}} Divide by 12.
{{{W^2 = 25}}} and...
{{{W = 5}}}ft. (Discard the negative solution from the square root).
{{{L = 3W}}}
{{{L = 15}}}ft.
So, to construct an open-top box with the foregoing dimensions, you would need to start with a rectangular sheet of cardboard with a length (l) of L+2h and a width (w) of W+2h, so...
{{{l = 15+2(4)}}}
{{{l = 23}}} and...
{{{w = W+2(4)}}}
{{{w = 5+8}}}
{{{w = 13}}}
The initial sheet of cardboard has to be 23ft. by 13ft, from which you would cut the four corners measuring 4ft. by 4ft.