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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

User MKorsch
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2 Answers

4 votes

EG=24 units i took the quiz

User Andrew Newby
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Answer:

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.




In parallelogramEFGH , EJ=x2−4 and JG=3x . What is EG ? 4 6 12 24 Quadrilateral E-example-1
User Jamie Dunstan
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