The value of x is the point of intersection of the graphs of [tex]\mathbf{P =12 + 2x}[/tex] and [tex]\mathbf{A =6x}[/tex]
The value of x is 3
The given parameters are:
[tex]\mathbf{Length = 6}[/tex]
[tex]\mathbf{Width = x}[/tex]
The perimeter is calculated as:
[tex]\mathbf{P =2 \times (Length + Width)}[/tex]
So, we have:
[tex]\mathbf{P =2 \times (6 + x)}[/tex]
Expand
[tex]\mathbf{P =12 + 2x}[/tex]
The area is calculated as:
[tex]\mathbf{P = Length \times Width}[/tex]
So, we have:
[tex]\mathbf{A =6 \times x}[/tex]
[tex]\mathbf{A =6x}[/tex]
See attachment for the graphs of [tex]\mathbf{P =12 + 2x}[/tex] and [tex]\mathbf{A =6x}[/tex]
From the attached graph, the lines of both functions meet at x =3.
Hence, the value of x is 3
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