Question

In a parallelogram EFGH, EJ=x^2-4 and JG=3x. What is EG?

Answer 1

EG = 24 ( solution is attached below)

Answer 2

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 = $x^2-4$

Side JG = 3x

According to the property of parallelogram,

Side EJ = Side JG

$x^2-4=3x$

$x^2-3x-4=0$

$x^2-4x+1x-4=0$

$x(x-4)+1(x-4)=0$

$(x-4)(x+1)=0$

(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 = $x^2-4+3x$

Now put the value of x = 4, we get:

Side EG = $(4)^2-4+3(4)=16-4+12=24$

Now put the value of x = -1, we get:

Side EG = $(-1)^2-4+3(-1)=1-4-3=-6$

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.