A gift box's rectangular base has a perimeter of 92 centimeters. The length of the base is one more than twice the base's width. Find the width (in centimeters) of this rectangular base.

Assume that the length of the rectangle is "l" and that the width is "w".

We are given that:

(1) The length is one more than twice the base. This means that:

l = 2w + 1 ... > equation I

(2) The perimeter is 92 cm. This means that:

92 = 2 (l+w) ... > equation II

Substitute with equation I in equation II to get the width as follows:

92 = 2 (l+w)

92 = 2 (2w+1+w)

92/2 = 3w + 1

46 = 3w + 1

3w = 46-1 = 45

w = 45/3

w = 15

Substitute with w in equation I to get the length as follows:

l = 2w + 1

l = 2 (15) + 1

l = 30 + 1 = 31

Based on the above calculations:

length of base = 31 cm

width of base = 15 cm