# Optimization Challenge 1

- Author:
- Tim Brzezinski

- Topic:
- Area, Calculus, Optimization Problems, Triangles

**In the applet below,**(This distance will change if you move point

*A*and*B*are 5 units apart.*B*, so keep it where it is for now.)

**Slide the green unlabeled slider.**What does this imply about the two lines? Nonetheless, the goal of this problem is to

**determine how far (to the left)**Even though you can use this applet to obtain an approximate value of this distance, use calculus to determine an

*D*needs to be placed from*C*in order to minimize total area enclosed by both triangles.*exact value*of this approximate distance. Retry this problem for

*AB*= some other distance. (You can move point

*B*to make this happen.)

**What if**

*AB*=*x*units? Can you find an expression (in terms of*x*) for the distance*DC*that minimizes the sum of the areas of both triangles?