The length of a rectangle is 3 cm more than four times the width. If the perimeter of the rectangle is 36 cm, what are its dimemions?

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Answer 1 · 2015-12-21T15:50:32

length#=10.5# #cm#
width#=7.5# #cm#

Start by making let statements to represent variables as the length and width as stated in the question.

Let #4x# represent the width.
Let #4x+3# represent the length.

#2[(4x)+(4x+3)]=36#
#2[8x+3]=36#
#8x+3=18#
#8x=15#
#x=15/8#

To find the dimensions, substitute #x=15/8# into #4x# (width) and #4x+3# (length).

Finding the width

#w=4x#

#w=4(15/8)#

#w=color(red)cancelcolor(black)4(15/color(red)cancelcolor(black)8^2)#

#w=15/2#

#w=7.5#

Finding the length

#l=4x+3#

#l=4(15/8)+3#

#l=color(red)cancelcolor(black)4(15/color(red)cancelcolor(black)8^2)+3#

#l=15/2+3#

#l=21/2#

#l=10.5#

#:.#, the length is #10.5# #cm# and the width is #7.5# #cm#.