VRZA is a parallelogram with sides #2x-4, 3y+5, 1/2 x +7 and y+12#. What is its perimeter?

1 Answer
May 11, 2018

Perimeter is #52 1/3#

Explanation:

In a parallelogram opposite sides are equal. Here in the parallelogram #VRZA#, sides are #2x-4#, #3y+5#, #1/2x+7# and #y+12# and pairs of opposite sides are (i) #2x-4# and #1/2x+7# and (ii) #3y+5# and #y+12#.

Hence #2x-4=1/2x+7#

or #2x-1/2x=7+4#

or #3/2x=11#

i.e. #x=11xx2/3=22/3#

and sides are #2x-4=2xx22/3-4=44/3-4=(44-12)/3=32/3# each

Similarly for other pair #3y+5=y+12#

or #2y=7# i.e. #y=7/2#

and sides are #3xx7/2+5=21/2+5=31/2# each

Hence perimeter is #(32/3+31/2)xx2#

= #(64+93)/6xx2#

= #157/3=52 1/3#