Question

In parallelogramEFGH , EJ=x2−4 and JG=3x . What is EG ? 4 6 12 24 Quadrilateral E F G H with lines bisecting the shape from E to G and from F to H, point where line segments E G and F H intersect is labeled J

Answer 1

EG=24 units i took the quiz

Answer 2

Option D is correct.

Side EG = 24 units.

Explanation:

As per the given statement:

In a parallelogram EFGH

`EJ = x^2-4` and
`JG = 3x`

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;

`x^2-4 = 3x`

⇒
`x^2-3x-4 =0`

⇒
`x^2-4x+x-4=0`

⇒
`x(x-4)+1(x-4)=0`

⇒
`(x+1)(x-4)=0`

By zero product property;

x = -1 and x = 4

⇒
`x =4` (always used positive number for sides)

Then;

EG = JG+JG = 2JG

`EG = 2JG = 2(3x) = 6x = 6 * 4 = 24` units

Therefore, the diagonal EG = 24 units.