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

What Function Best Represents The Perimeter Of The Orange Boxes class=

Sagot :

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

[tex]P=2l+2h[/tex]

FIRST BOX

For the first orange box, we have that:

[tex]\begin{gathered} l=x+x=2x \\ h=2 \end{gathered}[/tex]

Note that the box is divided into 2 parts.

Therefore, this perimeter is:

[tex]P_1=2(2x)+2(2)=2(2x)+4[/tex]

SECOND BOX

For the second orange box, we have that:

[tex]\begin{gathered} l=x+x+x=3x \\ h=2 \end{gathered}[/tex]

Note that the box is divided into 3 parts.

Therefore, the perimeter is:

[tex]P_2=2(3x)+2(2)=2(3x)+4[/tex]

Using the associative property of multiplication, we have that:

[tex]P_2=3(2x)+4[/tex]

Since x = 5, we have:

[tex]\begin{gathered} P_1=2(10)+4 \\ P_2=3(10)+4 \end{gathered}[/tex]

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:

[tex]P=10x+4[/tex]

ANSWER

The correct option is the THIRD OPTION.

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