Perimeter is simply the sum of the side lengths of a shape.
The true statement is:
(c) No. An absolute value equation will not work because the value of x would have to be negative for the perimeter to be 6 ft plus or minus 1.5 ft.
The perimeter of the rectangle is given as:
[tex]\mathbf{Perimeter = 6ft \± 1.5ft}[/tex]
The perimeter of a rectangle is:
[tex]\mathbf{Perimeter = 2 \times (Length + Width)}[/tex]
So, we have:
[tex]\mathbf{2 \times (Length + Width) = 6ft \± 1.5ft}[/tex]
Substitute values for length and width
[tex]\mathbf{2 \times (4 + x) = 6ft \± 1.5ft}[/tex]
Split
[tex]\mathbf{2 \times (4 + x) = 6ft + 1.5ft}[/tex] or [tex]\mathbf{2 \times (4 + x) = 6ft - 1.5ft}[/tex]
[tex]\mathbf{2 \times (4 + x) = 7.5ft}[/tex] or [tex]\mathbf{2 \times (4 + x) = 4.5ft}[/tex]
Divide both sides by 2
[tex]\mathbf{4 + x = 3.75ft}[/tex] or [tex]\mathbf{4 + x = 2.25ft}[/tex]
Solve for x
[tex]\mathbf{x = 3.75 - 4ft}[/tex] or [tex]\mathbf{x = 2.25 - 4ft}[/tex]
[tex]\mathbf{x = -0.25ft}[/tex] or [tex]\mathbf{x = -1.75ft}[/tex]
Both values of x are negative.
This means that; the absolute value model cannot work, because a rectangle cannot have a negative dimension.
Hence, option (c) is correct.
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