Suppose that you want to determine the width of the river below, but the current is too strong to cross the river. You stand away from the river at point B and sight a tree on the other side of the river at point E. You walk from point B straight towards the tree, stopping at point C by the river's edge. You then measure the distance from point C to point D, the spot on your side of the river that is directly across from the tree. You find CD = 21 feet. You return to point B and walk directly to the river's edge at point A. You measure this distance and find that AB = 10 feet. Finally, you measure and find AC = 13 feet. Note that this procedure ensures A-C-D, B-C-E, and that ∠A and ∠D are right angles. The width of the river is ED. Prove that ∆ABC ∼ ∆DEC, then determine the width of the river.