Andrew is designing a triangular bookcase for his friend. His blueprint shows that the bookcase is a right triangle with hypotenuse of length 14 meters, side length of x meters, and the other side length of 5 + x meters. What is the perimeter of the bookcase?

1212It is given that Andrew is dealing with a right triangle, so the Pythagorean theorem can be used to relate the side lengths to the hypotenuse. Substitute each value into the equation to produce an expression for x: , which can be expanded to , and rewriting as a quadratic , which can be solved using the quadratic formula to give x = -12.08 and x = 7.08 Notice that only 7.08 is a valid answer because side lengths cannot be negative. Also notice that it is the perimeter of the triangle that the question asks for: 7.08 + 5 + 7.08 + 14 = 33.16 meters.