Question 1046353
<font color=black size=3>L = length
W = width



"The length of a rectangle is 2 cm less than twice the width" means that {{{L = 2W-2}}}



Perimeter of rectangle = 2*(Length+Width)



{{{P = 2*(L+W)}}}



{{{P = 2*(2W-2+W)}}} Replace L with 2W-2



{{{P = 2*(3W-2)}}} Combine like terms



{{{P = 6W-4}}} Distribute



{{{P = 6W-4}}}



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We are told that the "perimeter is less than 66 cm", so the perimeter P is smaller than 66 meaning that {{{P < 66}}}



{{{P < 66}}} Start with the inequality



{{{6W-4 < 66}}} Replace P with 6W-4. Solve for W



{{{6W-4+4 < 66+4}}} Add 4 to both sides



{{{6W < 70}}} Combine like terms



{{{6W/6 < 70/6}}} Divide both sides by 6



{{{W < 11.6666666666667}}} Simplify



Since W is less than {{{11.6666666666667}}}, this means that the largest W can be is {{{W = 11}}}



The maximum width is <font color=red>11 cm</font></font>