Question 112250
Remember, the perimeter of a rectangle is {{{P=2W+2L}}}



{{{24=2(3)+2(3x)}}} Plug in the given perimeter, length and width



{{{24=6+6x}}} Plug in the given perimeter, length and width




{{{0=6+6x-24}}}Subtract 24 from both sides



{{{-6x=6-24}}} Subtract 6x from both sides



{{{-6x=-18}}} Combine like terms on the right side



{{{x=(-18)/(-6)}}} Divide both sides by -6 to isolate x




{{{x=3}}} Divide


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Answer:

So our answer is {{{x=3}}}



{{{3*3=9}}} Now plug in {{{x=3}}} into {{{3x}}}



So the width is 9


Check:


{{{P=2W+2L}}} Start with the given formula



{{{24=2(9)+2(3)}}} Plug in P=24, W=9 and L=3



{{{24=18+6}}} Multiply



{{{24=24}}} Add. Since both sides are equal, our answer is verified.