A right triangle's hypotenuse is 1 cm longer than twice the length of the shortest side.
The third side is 1 cm less than twice the shortest side.
Find the length (in cm) of the hypotenuse.

Answer:   17 cmStep-by-step explanation:You want the hypotenuse (c) in a right triangle that has c=2a+1, b=2a-1.Pythagorean theoremThe relation between the side lengths in the right triangle is ...   a² +b² = c²ApplicationSubstituting the given relations, we have ...   a² +(2a-1)² = (2a+1)²   a² +4a² -4a +1 = 4a² +4a +1   a² -8a = 0 . . . . . . write in standard form   a(a -8) = 0 . . . . . . factor   a = 0 or a = 8We are almost never concerned with triangles that have 0 area, so the solution of interest is a=8. Then the hypotenuse is ...   c = 2(8) +1 = 17The hypotenuse is 17 cm.__Additional commentYou may recognize these side lengths as the (8, 15, 17) Pythagorean triple.