the perimeter ofa rectangle is 16 times the width. the length is 12 cm more than the width. find the lenght and width of the rectangle

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first you set up the equation like this: 2l + 2w = p = 16w [the length (l) and the width (w) multiplied by 2 then added together equals the perimeter which is in turn equal to w*16 or 16w] remove p from the equation since it is just there to help you set up the following equation: 2l + 2w = 16w the problem also says that l = w+12 so substitute the l in the equation with w+12: 2(w+12) + 2w = 16w simplify: 2w + 24 + 2w => 4w + 24 = 16w then you isolate the width (bring the w to one side of the equation): 12w=24 divide each side by 12 to get w by itself and you find that w=24/12 or =2 then go add 12 to 2 to find the length (2+12=14) as with any problem, you might want to check that the answer works completely, so plug both numbers into the original perimeter equation: 2(12) + 2(2)= p = 32 32 is 16 times more than 2 the width so the problem works.