Polynomial

Question

On a map, Detroit, Michigan, Ann Arbour, Michigan and Toledo, Ohio form the vertices of a right triangle. The distance between Ann Arbour and Toledo is 11 miles more than distance between Ann Arbour and Detroit. The distance between Toledo and Detroit is 22 miles more than the distance between Ann Arbour and Detroit. Find the distance bwteen Ann Arbour and Detroit

Answer 1

Let x represent the distance between Ann Arbor and Detroit, x+11 represent the distance between Ann Arbor and Toledo and x+22 represent the distance between Toledo and Detroit. Since the cities lie on the vertices of a right triangle, we can use the Pythagorean Theorem.

            x² + (x+11)² = (x+22)²

   x² + x² + 22x + 121= x² + 44x + 484  Arrange all of the terms on one side to get x² - 22x - 363 = 0   Factor the trinomial to get

              (x+11)(x-33) = 0.  The solutions to the equation are x = -11 and x = 33. Since it does not make sense for the distance to be negative, disregard -11. Therefore the distance between Ann Arbor and Detroit is 33 miles.