The perimeter of a rectangle is 44 cm. If the length is two less than triple the width, what is the width?

1 Answer
Dec 24, 2017

See a solution process below:

Explanation:

We can write a relationship between the width and length as:

#l = 3w - 2"cm"#

The formula for the perimeter of a rectangle is:

#p = 2(l + w)#

We can substitute #44"cm"# for #p# and #(3w - 2"cm")# for #l# and solve for #w#:

#44"cm" = 2((3w - 2"cm") + w)#

#44"cm" = 2(3w - 2"cm" + w)#

#44"cm" = 2(3w + w - 2"cm")#

#44"cm" = 2(3w + 1w - 2"cm")#

#44"cm" = 2([3 + 1]w - 2"cm")#

#44"cm" = 2(4w - 2"cm")#

#44"cm" = (2 xx 4w) - (2 xx 2"cm")#

#44"cm" = 8w - 4"cm"#

#44"cm" + color(red)(4"cm") = 8w - 4"cm" + color(red)(4"cm")#

#48"cm" = 8w - 0#

#48"cm" = 8w#

#(48"cm")/color(red)(8) = (8w)/color(red)(8)#

#6"cm" = (color(red)(cancel(color(black)(8)))w)/cancel(color(red)(8))#

#6"cm" = w#

#w = 6"cm"#