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Parallelogram L O N M is shown. Diagonals are drawn from point L to point N and from point O to point M and intersect at point Q. The length of line segment O Q is (2 x + 3) centimeters and the length of lines segment Q M is (3 x minus 4) centimeters. In parallelogram LONM, what is OM? 7 cm 17 cm 24 cm 34 cm

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The length of line segment OM is 34 cm.

Step-by-step explanation:

  • The diagonals of a parallelogram bisect each other (cuts equally into two halves).
  • The line segment OM is a diagonal with an intersection point Q.
  • The line segment OQ is equal in length as the line segment QM.

Step 1 :

⇒ length of OQ = length of QM

⇒ 2x + 3 = 3x -4

⇒ 3x-2x =4+3

⇒ x = 7

Step 2 :

Subsitute x = 7 in OQ and QM

⇒ length of OQ = 2x+3

⇒ 2(7) + 3 = 17 cm

⇒ length of QM = 3x-4

⇒ 3(7) - 4 = 17 cm

∴ Length of OM = length of OQ + length of QM

⇒ OM = 17+17 = 34 cm

Answer:

D-34

Step-by-step explanation:

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