Answer : The value of side EG is, 24 units.
Step-by-step explanation :
Property of parallelogram:
The diagonals bisect each other and the opposite sides are equal to each other.
In the given parallelogram EFGH,
Given:
Side EJ = [tex]x^2-4[/tex]
Side JG = 3x
According to the property of parallelogram,
Side EJ = Side JG
[tex]x^2-4=3x[/tex]
[tex]x^2-3x-4=0[/tex]
[tex]x^2-4x+1x-4=0[/tex]
[tex]x(x-4)+1(x-4)=0[/tex]
[tex](x-4)(x+1)=0[/tex]
(x-4) = 0 and (x+1) = 0
x = 4 and x = -1
Now we have to determine the value of side EG.
Side EG = Side EJ + Side JG
Side EG = [tex]x^2-4+3x[/tex]
Now put the value of x = 4, we get:
Side EG = [tex](4)^2-4+3(4)=16-4+12=24[/tex]
Now put the value of x = -1, we get:
Side EG = [tex](-1)^2-4+3(-1)=1-4-3=-6[/tex]
As we know that, the value of side can not be negative. So, the value of side EG will be, 24 units.
Hence, the value of side EG is, 24 units.
