A triangle has vertices at 0600 and 120 Find the rectangle w

Solution

Here are the steps:

1. Draw your triangle and now draw the rectangle inside the triangle with the bottom left corner at the origin and the top right corner on the decreasing line y = (-1/2) x + 6

2. You want to maximize A = x y. This is the thing you want to take the derivative of, set that derivative = 0 and find the critical points. Problem is that there are two variables in this equation and we only know how to take derivatives when there is one letter.

3. To handle this, substitute (-1/2) x + 6 in for y. Distribute the x into the parens and take an easy derivative. Set equal to 0 to find the critical point but in general with problems like these there is only one answer which makes sense. (i.e., the rectangle inscribed with minimum area is to make no rectangle at all).