Answer:
The required length of [tex]EJ[/tex] is [tex]24[/tex] units.
Step-by-step explanation:
Given: In parallelogram [tex]EFGH, EJ=x^2-4[/tex] and [tex]JG=3x[/tex].
we know that
In a parallelogram; opposite sides are equal, opposite angles are equal and diagonals bisect each other.
From the figure,
[tex]EJ=EJ+JG[/tex]
And [tex]EJ=JG[/tex] ( diagonals of parallelogram bisect each other )
[tex]x^2-4=3x\\x^2-3x-4=0\\x^2-4x+x-4=0\\x(x-4)+1(x-4)=0\\(x-4)(x+1)=0\\x-4=0\rm\;\;(or)\;\; x+1=0\\x=4\; \rm\;(or)\; \;x=-1[/tex]
Neglecting the value of [tex]x=-1[/tex] as length cant be negative.
Therefore,
[tex]EJ=JG+JG\\EJ=2JG\\EJ=2\times3\times4\\EJ=24[/tex]
Hence, the length of [tex]EJ[/tex] is [tex]24[/tex] units.
For more information:
https://brainly.com/question/11560033?referrer=searchResults
