Answer:
Option D is correct.
Side EG = 24 units.
Step-by-step explanation:
As per the given statement:
In a parallelogram EFGH
[tex]EJ = x^2-4[/tex] and [tex]JG = 3x[/tex]
By Properties of parallelogram:
- Two diagonals bisects each other and
- Each diagonal of a parallelogram separates it into two congruent.
Here, EG and FH are diagonals;
EG = EJ + JG
by properties of parallelogram:
EJ =JG
Substitute the given values we have;
[tex]x^2-4 = 3x[/tex]
⇒[tex]x^2-3x-4 =0[/tex]
⇒[tex]x^2-4x+x-4=0[/tex]
⇒[tex]x(x-4)+1(x-4)=0[/tex]
⇒[tex](x+1)(x-4)=0[/tex]
By zero product property;
x = -1 and x = 4
⇒[tex]x =4[/tex] (always used positive number for sides)
Then;
EG = JG+JG = 2JG
[tex]EG = 2JG = 2(3x) = 6x = 6 \times 4 = 24[/tex] units
Therefore, the diagonal EG = 24 units.
