A construction crew has to dig ditches for a set of pipes that must carry water from point A to both of points B and C see figure Points B and Care 4 km apart and point A is 4 km from the midpoint of B and C They want to dig as little as possible and they believe the best way to do that is to dig from point A to some point D along the midline a distance h from the midpoint of B and C They know that they should choose h satisfying 05h2 but they are not sure exactly what value of h to use 4 km 4 km B D a Formulate an expression h for the total length of ditch b Now calculate the value of which minimizes the amount of ditch to be dug If there is more than one such value give your answer as a comma