We know that in a rectangle the opposite sides will be equal in length. Thus, we will have [tex] LM=ON [/tex] and [tex] LO=MN [/tex]. Since we are interested only in finding the value of the variable y, we will take the equation:
[tex] LM=ON [/tex]
Now, from the diagram, [tex] LM=3y-6 [/tex] and [tex] ON=2y+4 [/tex] . Thus, we get:
[tex] 3y-6=2y+4 [/tex]
Rearranging and simplifying we get:
[tex] 3y-2y=6+4 [/tex]
[tex] \therefore y=10 [/tex]
Thus, the solution for y is 10.
