Question

A box with an open top has a square base and four sides of equal height. The volume of the box is 539 ft^3. The height is 4 ft greater than both the length and the width. If the surface area is 357 ft^2, what are the dimensions of the box?

Answer 1

A box with an open-top has a square base and four sides of equal height.

The volume of the box is 539 ft^3.

The surface area is 357 ft^2

Let H is the height, L is the length and W is the width.

The volume is given by

$\begin{gathered} V=L\cdot W\cdot H \\ 539=L\cdot W\cdot H \end{gathered}$

The height is 4 ft greater than both the length and the width.

$W=L=H-4$

The surface area is given by