katiek0193
Answered

In the figure below,

PT = 2x

TR = y + 4

QT = x + 2

and TS = y


(picture attached below)


find the values of x and y in parallelogram PQRS.

Ax = 2, y = 4
Bx = 0, y = 2
Cx = 6, y = 8
Dx = 4, y = 6

thanks in advance! :)

In the figure below, PT = 2x TR = y + 4 QT = x + 2 and TS = y (picture attached below) find the values of x and y in parallelogram PQRS. A. x = 2, y = 4 B. x = class=

Verified Answer :

The answer is C. x = 6, y = 8

netlarue98

Answer:

x = 6, y = 8

Step-by-step explanation:

The diagonals of a parallelogram bisect each other.  \(\frac{PT}{QT}\) ≅ \(\frac{TR}{ST}\)

  • Set up a system of linear equations by substituting the algebraic expressions for each segment length. \(\frac{2x}{x+2 }\) ≅ \(\frac{y+4}{y}\)     (Notice y = x+2)
  • Substitute (x+2) for y, then solve for x.

       2x = (x+2) + 4

       2x = x + 6 (subtract x from both sides)

       x = 6

  • Substitute 6 for x, then solve for y.

       2(6) = y + 4

       12 = y + 4 (subtract 4 from both sides)

       y = 8

So, x = 6, y = 8

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