Question

What function best represents the perimeter of the orange boxes? *

Answer 1

The formula used to calculate the perimeter of a rectangle is given to be:

`P=2l+2h`

FIRST BOX

For the first orange box, we have that:

`\begin{gathered} l=x+x=2x \\ h=2 \end{gathered}`

Note that the box is divided into 2 parts.

Therefore, this perimeter is:

`P_1=2(2x)+2(2)=2(2x)+4`

SECOND BOX

For the second orange box, we have that:

`\begin{gathered} l=x+x+x=3x \\ h=2 \end{gathered}`

Note that the box is divided into 3 parts.

Therefore, the perimeter is:

`P_2=2(3x)+2(2)=2(3x)+4`

Using the associative property of multiplication, we have that:

`P_2=3(2x)+4`

Since x = 5, we have:

`\begin{gathered} P_1=2(10)+4 \\ P_2=3(10)+4 \end{gathered}`

where 2 and 3 are the number of divisions of the boxes.

If we represent the number of divisions with x, we have the perimeter's function to be:

`P=10x+4`

ANSWER

The correct option is the THIRD OPTION.