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Answer 1 · 2018-01-03T06:17:18

length = #10 cm# and width = #6cm#

Suppose the width of the rectangle = #x cm#
Then, the length of the rectangle = #x+4 cm#

Now, the changes to the length and width of the rectangle are as below:

Length is decreased by #5cm#, then the new length will be:
#x+4 -5cm# = #x-1 cm#

The width is decreased by #2 cm#, then the new width will be:
#x-2 cm#

The perimeter of this new rectangle = #18 cm#

Perimeter of rectangle = #2(l+w)#
where, #l# = length, and #w#= width

So, #18# = #2 xx[(x-1)+(x-2)]#
or, #18# = #2xx(2x-3)# = #4x-6#

or, #18# = #4x-6#

or, # 18+6# = #4x#

or, #x# = #24/4# = #6 cm# (width)

and length = #x+4 cm# = #6+4 cm# = #10 cm#