Question

The width of a rectangle measures (5.5d+9.7f)(5.5d+9.7f) centimeters, and its length measures (5.1d-3.5f)(5.1d−3.5f) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? A. 21.2d+12.4 B. 9.7−7f+21.2d C. 21.2d+12.4f D. 6.2+10.6d

Answer 1

Answer: C. 21.2d+12.4f

Step-by-step explanation:

Given, The width of a rectangle measures$(5.5d+9.7f)$  centimeters, and its length measures $(5.1d-3.5f)$ centimeters.  

Perimeter of rectangle = 2 (length + breadth)

$= 2 ((5.5d+9.7f)+ (5.1d-3.5f) )\\\\=2 (5.5d+9.7f+5.1d-3.5f)\\\\= 2(5.5d+5.1d+9.7f-3.5f)\ \ \ [\text{Combine like terms}]\\\\= 2(10.6d+6.2f)\\\\= 21.2d+12.4f\ \ \ [\text{Multiply 2 inside the bracket}]$

Hence, the correct option is C. 21.2d+12.4f .