Question

I have to write a polynomial that represents the perimeter including the frame. I don’t know how please help

Answer 1

The base of the picture is 16 inches, when you add the frame there is an additional "x"

Base = 16 + x

The height of the picture is 20 inches, when you add the frame there is an additional "x".

Base = 20 + x

Perimeter = 2(base) + 2(height)

                 = 2(16 + x) + 2(20 + x)

                 = 32 + 2x   +  40 + 2x

                 = 72 + 4x

Answer: (72 + 4x) inches

Answer 2

The inner dimensions are 16 and 20 inches. The frame consists in x extra inches along both dimensions, so the extended dimensions are 16+x and 20+x inches.

Now, the perimeter of a rectangle is twice the sum of the dimension, so your perimeter is

$2(16+x + 20+x) = 2(2x+36) = 4x + 72$