Answer:
24
Explanation:
Given right triangle sides x, 2x-3, and 2x+3, you want to know the length of the side labeled x.
Pythagorean theorem
The Pythagorean theorem tells you the square of the hypotenuse is equal to the sum of the squares of the other two sides.
(2x +3)² = (2x -3)² +x²
4x² +12x +9 = 4x² -12x +9 +x²
x² -24x = 0 . . . . . subtract 4x² +12x +9
x(x -24) = 0 ⇒ x = 0 or 24
The length of the side labeled x is 24 units.
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Additional comment
The triangle is an 8-15-17 triangle scaled up by a factor of 3.