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?

21.2d + 12.4f

Step-by-step explanation:

Given that:

Width of rectangle = (5.5d+9.7f) centimeters

Length of rectangle = (5.1d-3.5f) centimeters

Perimeter of a rectangle : 2 (length + Width)

2 [(5.1d-3.5f) + (5.5d+9.7f)]

2[5.1d - 3.5f + 5.5d + 9.7f]

2[10.6d + 6.2f]

= 21.2d + 12.4f

Hence, the perimeter is :

21.2d + 12.4f)

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)