For a big dinner, Savannah needs to attach an extra piece to her dining room table. Without the extra piece, the table is 6 feet long and 3 feet wide. Attaching the extra piece to the table adds x feet to its length.
Pick all the expressions that represent the area of the table with the extra piece.
a. x(6+3)
b. 3(6+x)
c. 18+3x
d. 18+6x
To find the area of the table with the extra piece, we need to multiply its new length by its width.
The width of the table remains unchanged at 3 feet.
The new length of the table becomes 6 + x feet, because x feet are added to the original length of 6 feet.
Hence, the area of the table with the extra piece is (new length) x (width), or (6 + x) * 3.
Now let's evaluate the given expressions to see which ones are equivalent to this:
a. x(6+3) = 6x + 3x = 9x
This does not correctly represent the area because it only accounts for x times the sum of the length and width and does not include the base area of the table.
b. 3(6+x) = 18 + 3x
This correctly represents the area of the table with the extra piece.
c. 18+3x
This is the same as expression b, and also correctly represents the area of the table with the extra piece.
d. 18+6x
This expression incorrectly represents the area because it adds 6 times the additional length to the original area, which would mean the width is being multiplied by 6, not by 3.
The correct expressions for the area of the table with the extra piece are b and c, which are:
b. 3(6+x)
c. 18+3x
pick one
Apologies for the confusion. While b and c represent the same mathematical value, due to the format of the question, you should select one expression as the answer. In this case, pick:
b. 3(6+x)
which explicitly shows the original width (3 feet) multiplied by the sum of the original length (6 feet) and the additional length (x feet).
To find the area of the table with the extra piece, we need to multiply the length and width of the table.
The length of the table without the extra piece is 6 feet. When the extra piece is attached, it adds x feet to the length. Therefore, the total length of the table with the extra piece is 6 + x.
The width of the table remains 3 feet.
To find the area, we multiply the length and width:
Area = Length × Width
So the expressions that represent the area of the table with the extra piece are:
a. x(6 + 3) - This expression is incorrect because it multiplies x with the sum of 6 and 3, which doesn't give us the area.
b. 3(6 + x) - This expression is correct because it multiplies 3 with the sum of 6 and x, which gives us the area.
c. 18 + 3x - This expression is incorrect because it adds 18 to 3x, which doesn't give us the area.
d. 18 + 6x - This expression is incorrect because it adds 18 to 6x, which also doesn't give us the area.
So, the correct expression is b. 3(6 + x).