The hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle. The shorter side of the triangle is 7 centimeters less than the longer side. Find the length of the hypotenuse.	Choose one:
A) 17	B) 18	C) 19	D) 20	E) 21

Rationale: let a and b be the two sides of the triangle such that a is longer than b . the statement ` ` the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle ' ' may be fomulated by h = a + 2 or a = h - 2 the statement ` ` the shorter side of the triangle is 7 centimeters less than the longer side ' ' may be formulated . b = a - 7 or b = ( h - 2 ) - 7 = h - 9 we now use pythagora ' s theorem to write a third equation h 2 = a 2 + b 2 substitute a by h - 2 and b by h - 9 in the above equation to obtain an equation in one variable only . h 2 = ( h - 2 ) 2 + ( h - 9 ) 2 simplify and rewrite the above equation in standard form . h 2 - 22 h + 85 = 0 solve for h . h = 5 and h = 17 . only the solution h = 17 gives a and b positive and it is the length of the hypotenuse of the triangle . answer a
Answer: A