Lenght/Width problem

Question

Sally must decorate the perimeter of two tables. One is square, and the other is rectangular with length three times the width. She has 70 feet of trim. What dimensions should the

tables be to maximize their total area?

Answer 1

Here is another exercise in arithmetic which obscures the point of the problem.

The perimeter of the square is 4s and the perimeter of the rectangles is 8w.

4s + 8w = 70

The area is s² +3w²

Use the perimeter equation to get a relation between w and s, e.g.

s=.5(35-4w).

Now substitute the expression for s into the area equation.

Differentiate the expression for area with respect to w.

Set this derivative equal to 0 and solve for w.

The get both 3w an and s.