Based on the calculations, the resulting three-dimensional shape is: C. a cylinder with a base radius of 17 units.
In Geometry, when a rectangle is rotated about a line, it produces a three-dimensional shape (figure) referred to as a cylinder. Also, the width of this rectangle is equal to the radius of the cylinder.
Thus, we would determine the width of this rectangle by using the formula for perimeter, so as to find the radius of the cylinder.
Mathematically, the perimeter of a rectangle is given by the formula;
P = 2(L + W)
82 = 2(24 + W)
82 = 48 + 2W
2W = 82 - 48
2W = 34
W = 17 units.
Read more on perimeter of a rectangle here: brainly.com/question/17297081
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