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The length of a rectangle is 1 in. less than 3 times the width. If the perimeter of the rectangle is 46 in., find the length and the width.

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[tex] \Large {\mathbb {SOLUTION: }}[/tex]

[tex] \: \: \text{L = 3w - 1}[/tex]

[tex] \: \: \text{P=46}[/tex]

[tex] \: \: \text{2(3w-1) + 2w = 46}[/tex]

[tex] \: \: \text{6w - 2 + 2w = 46}[/tex]

[tex] \: \: \text{8w = 48}[/tex]

[tex] \: \: \text {W = 6 }[/tex]

[tex] \: \: \text{L = 17}[/tex]

[tex] \: \: \text{Applying the inequalities:}[/tex]

[tex] \: \: \text{L>=17 and w=6}[/tex]

[tex] \: \: \text{The perimeter is at least 46.}[/tex]

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