Consider a rectangle inscribed in an equilateral triangle with sides / = 20. We want to determine the dimensions of the rectangle with largest area that can be inscribed inside the triangle. The area of the rectangle, as a function of and y is A x = 1 Now, A'(x) = Solving for and, ultimately for y, yields I y = Use the substitution principle to rewrite the area as a function of . (Hint: Similar Triangles) A = A(z) = To determine optimal values, we need to look at A'(x) = 0. inches y inches Note: What is the maximum area? A = h=121 square inches