Respuesta :

absor201

Answer:

We conclude that:

  • The value of x = 7
  • The value of y = 4

Step-by-step explanation:

Given

  • The parallelogram PQRS

We know that the diagonals of a parallelogram bisect each other.

so

[tex]RT = TP[/tex]

Given

  • RT = x
  • TP = 5x-28

so substituting RT = x, and TP = 5x-28

[tex]RT = TP[/tex]

[tex]x = 5x-28[/tex]

[tex]5x = x+28[/tex]

[tex]5x-x = 28[/tex]

[tex]4x = 28[/tex]

divide both sides by 4

[tex]4x/4 = 28/4[/tex]

[tex]x = 7[/tex]

Therefore, the value of x:

  • x = 7

Similarly,

[tex]QT = TS[/tex]

Given

  • QT = 5y
  • TS = 2y+12

so substituting QT = 5y, and TS = 2y+12

[tex]QT = TS[/tex]

[tex]5y = 2y+12[/tex]

[tex]5y-2y = 12[/tex]

[tex]3y = 12[/tex]

divide both sides by 3

[tex]3y/3 = 12/3[/tex]

[tex]y = 4[/tex]

Therefore, the value of y:

y = 4

Therefore, we conclude that:

  • The value of x = 7
  • The value of y = 4

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