In his arts and crafts class, Tony is given a piece of paper and asked to make a rectangular box. The length of the box he created is 3 times of its width. His friends made boxes with various lengths, widths and heights. He wonders how the height changes affects the width.

What is known:

• The surface area of the box is constant at 100 in².
• The length is 3 times of its width.

What is the rate of change of the width with respect to the enlarge of height?

• Find the relationship between the width and the height.
• Apply implicit differentiation method