# Unknown Perimeter Of A Parallogram - Subsitution Equation?

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# Unknown Perimeter Of A Parallogram - Subsitution Equation?

The perimeter of parallogram JCSE is 219 more than the length of side JC and 177 more than the length of side CS.  What is the length of side SE?
I've tried algebraic equations with substution.  I know the answer is 45 and the other side is 87 but I have no idea how to get it!

March 9, 2009, 3:54 pm by Kickcycle111

lets take the side JC  as  ‘a ‘ and the side CS as ‘b’. Lets take the perimeter as p.
So p = 219+a = 177 + b
Now  rearranging the variables to one side  b - a = 219 - 177
b - a = 42   --------- eqn 1.
Also  p = 2 ( a + b ) which is equal to 219 + a
So  2 ( a + b ) = 219 + a
2a + 2b  =  219 + a
so     2a-a    =   219 - 2b
a   =   219 - 2b
Substitute the value of ‘a’ in the equation 1
Now    b - ( 219 - 2b ) = 42
b -  219 + 2b  = 42
3b =  42 +  219
b   =  261/3
b = 87
So ‘a’ will  be 87 - 42 = 45  by substituting in the equation 1

March 17, 2009, 12:13 am by Guest