Answer:
17 cm
Explanation:
You want the hypotenuse (c) in a right triangle that has c=2a+1, b=2a-1.
Pythagorean theorem
The relation between the side lengths in the right triangle is ...
a² +b² = c²
Application
Substituting 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 = 8
We 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 = 17
The hypotenuse is 17 cm.
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Additional comment
You may recognize these side lengths as the (8, 15, 17) Pythagorean triple.