Question

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.

Answer 1

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.