A rectangle has a length of (3.2a + 0.18b) centimeters. The width is half the length. Sasha writes the expression (12.8a + 0.72b) to represent the perimeter of the rectangle in centimeters. Is Sasha's reasoning correct? Explain.

The width is half the length, so is

width = (1/2) * length

width = (1/2) * (3.2a + 0.18b) cm

width = (1.6a + 0.09b) cm

The perimeter of the rectangle is twice the sum of length and width.

perimeter = 2 * (length + width)

perimeter = 2 * ((3.2a + 0.18b) cm + (1.6a + 0.09b) cm)

perimeter = 2 * (4.8a + 0.27b) cm)

perimeter = (9.6a + 0.54b) cm

Sasha did not get this answer, so apparently ...

her reasoning was not correct.