SOLUTION: the length of a rectangular label is 3 cm less than twice the width .the perimeter is 54 cm .find the width

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Question 1059393: the length of a rectangular label is 3 cm less than twice the width .the perimeter is 54 cm .find the width
Answer by Theo(13342) (Show Source):
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l equals the length.
b equals the width.

perimeter equals 2 times the length + 2 times the width
p = 2l + 2w

length equals 3 cm less than twice the width.
l = 2w - 3

p = 2l + 2w becomes p = 2 * (2w-3) + 2w.
simplify to get p = 4w - 6 + 2w.
combine like terms to get p = 6w - 6

since p = 54 cm, this becomes 54 = 6w - 6
add 6 to both sides to get 60 = 6w
solve for w to get w = 10
l is equal to 2w-3 so l = 17.

p = 2l + 2w becomes p = 2*17 + 2*10 which makes p = 34 + 20 which makes p = 54.

solution appears to be that width = 10 cm.