SOLUTION: A rhombus has sides which are x-y, 2x+y+1 and 3x-y-2/2. Find : a) the length of a side b) the perimeter of the rhombus

Algebra ->  Parallelograms -> SOLUTION: A rhombus has sides which are x-y, 2x+y+1 and 3x-y-2/2. Find : a) the length of a side b) the perimeter of the rhombus      Log On


   

Question 925247: A rhombus has sides which are x-y, 2x+y+1 and 3x-y-2/2.
Find :
a) the length of a side
b) the perimeter of the rhombus
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Rhombus is a parallelogram with 4 equal sides.
Parallelogram has opposite sides parallel.

if a rhombus has sides which are:
x-y, 2x%2By%2B1 and %283x-y-2%29%2F2, then
x-y=2x%2By%2B1....(1)
x-y=%283x-y-2%29%2F2....(2)
___________________.....solve this system
x-y=2x%2By%2B1....(1)...solve for x
-y-y-1=2x-x
-2y-1=x.....substitute in (2)

-2y-1-y=%283%28-2y-1%29-y-2%29%2F2...solve for y
-3y-1=%28-6y-3%29-y-2%29%2F2
-3%2A2y-1%2A2=-6y-3-y-2
-6y-2=-7y-5
7y-6y=2-5
highlight%28y=-3%29
find x
-2y-1=x
x=-2%28-3%29-1
x=6-1
highlight%28x=5%29
a) the length of a side
x-y=5-%28-3%29
x-y=5%2B3
highlight%28x-y=8%29
b) the perimeter of the rhombus
P=4%2A8
highlight%28P=32%29