The length of a rectangular piece of steel in a bridge is 2 meters less than triple the width. The perimeter of the piece of steel is 36 meters. How do you find the length of the piece of steel?

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Answer 1 · 2015-10-04T15:29:37

Length of the Steel piece is #"13 m"#

Let the width be equal to #w# meters. The length is #2# meters less than triple the width. So the length of the steel piece is

#l = 3w - 2#

Now the perimeter of a rectangle is given by

#P = 2 * (l + w)" "#, where

#l# is the length
#w# is the width.

In this case, the perimeter will be

#P = 2 * (underbrace(3w - 2)_(color(blue)(=l)) + w)#

#P = 2 * (4w - 2) = "36 m" -># given

So

#2 *(4w - 2) = 36#

#4w - 2 = 36/2 = 18#

#4w = 18 + 2 = 20 implies w = 20/4 = "5 m"#

The length is

#l = 3 * 5 - 2 = "13 m"#