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If ON=5X-7,LM=4X+4NM=X-7 and OL=3Y-4 find the values of x and y for which LMNO must be a parallelogram. The diagram is not to scale.

Ax = 11,y = 8/3
Bx = 4,y = 3/8
Cx = 11,y = 3/8
Dx = 4,y = 8/3

If ON=5X-7,LM=4X+4NM=X-7 and OL=3Y-4 find the values of x and y for which LMNO must be a parallelogram. The diagram is not to scale. a. x = 11,y = 8/3 b. x = 4, class=

Verified Answer :

James98

The answer is a.

5x-7 = 4x+4   solve for x

substitute  x in (x-7) to get 11-7

3y-4 = 11-7    solve for y

To find the value of x and y we should know the properties of the Parallelogram.

Parallelogram

A parallelogram is a quadrilateral, whose opposite sides are always parallel and equal to each other.

Given to us

  • ON=5X-7,
  • LM=4X+4,
  • NM=X-7,
  • OL=3Y-4


Solution

For the quadrilateral LMNO to be a parallelogram the opposite sides of the parallelogram must be equal to each other. Therefore,

  1. LM = ON, and
  2. OL = NM.

Equation 1

Substituting the value in equation 1,

\(LM = ON\\ 4x+4 =5x-7\\ 4x-5x =-7-4\\ -x =-11\\ x = 11\)

Equation 2

Substituting the value in equation 2,

OL = NM

\(3y-4=x-7\)

Substituting the value of x

\(3y-4=(11)-7\\ 3y-4=11-7\\ 3y = 11-7+4\\ 3y = 8\\ y=\dfrac{8}{3}\)

Hence, the value of x and y should be 11 and  \(\dfrac{8}{3}\) for LMNO to be a parallelogram.

Learn more about Parallelogram:

https://brainly.com/question/1563728

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