The width of a rectangular box is 20% of the length. If the perimeter is 192 cm, then what are the length and width of the box?

1 Answer
Jul 6, 2017

Answer:

length#=80cm#

Explanation:

Let the width be #w#
Let the length be #L#
Let perimeter be #p#

Drop the units of measurement for now

Then #p=2w+2L = 2(w+L)#

but #w=20/100L# so by substitution we have:

#p=192=2(20/100L+L)#

Factor out #L#

#192=2L(20/100+1)#

but #20/100+1# is the same as #20/100+100/100=120/100#

#192=cancel(2)^1L(120/(cancel(100)^50))#

#L=192xx50/120=80#

#L=80cm#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
check

width = #20/100L = 20/100xx80=16#

#2w+2L->2(80)+2(16)=192# as required