a poster reproduces the Mona Lisa in the original size, but adds a 4 1/2 inch border around each side. What is the perimeter of this poster if the length is 30 3/10" and width is 20 7/8"?

Not clear if the dimensions given shows the poster before or after the border is added.

anyway, 9 inches were added both the length and the width, so you take it from there.
Might be a good idea to make a sketch to see why you would add 4.5 twice.

the dims are of the poster and then he adds 4 1/2 inch

So, follow the instructions that I gave you, let me know what you got.

we got 119 3/20 for the perimeter

old width = 20.875

new width = 20.875 + 9 = 29.875

old length = 30.3
new length = 30.3+9 = 39.3

new perimeter
= 2(width + length)
= 2(30.3+39.3) = 138.35

in fraction form that would be 138 7/20

I have no idea how you could have come up with your answer if you followed my instructions.

last calculations should say:

new perimeter
= 2(width + length)
= 2(29.875+39.3) = 138.35

in fraction form that would be 138 7/20

To find the perimeter of the poster, we need to add up all the sides.

First, let's calculate the actual size of the Mona Lisa reproduction without the added border.

Length: 30 3/10" = 30 + 3/10 = 300/10 + 3/10 = 303/10"
Width: 20 7/8" = 20 + 7/8 = 160/8 + 7/8 = 167/8"

Now, let's calculate the size of the reproduction with the added border.

Length with border: 30 3/10" + 4 1/2" + 4 1/2" = 30 3/10" + 9" = 30 + 3/10 + 90/10 = 120/10 + 3/10 + 90/10 = 213/10"
Width with border: 20 7/8" + 4 1/2" + 4 1/2" = 20 7/8" + 9" = 20 + 7/8 + 72/8 = 160/8 + 7/8 + 72/8 = 239/8"

To find the perimeter, we add up all the sides:

Perimeter = 2 * (Length with border + Width with border)
= 2 * (213/10" + 239/8")

To add these mixed numbers, we first convert them to improper fractions:

Perimeter = 2 * (213/10 + 239/8)

To add fractions with different denominators, we find a common denominator:

Perimeter = 2 * (213/10 * 8/8 + 239/8 * 10/10)
= 2 * (1704/80 + 2390/80)
= 2 * (4094/80)

Now, let's simplify the fraction:

Perimeter = 2 * (2047/40)
= 4094/40

Finally, let's simplify the fraction and convert it back to a mixed number:

Perimeter = 102 17/20"

Therefore, the perimeter of the poster is 102 17/20" or 102.85 inches.