Question

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 = 0, y = 2
C. x = 6, y = 8
D. x = 4, y = 6

thanks in advance! :)

Answer 1

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

Answer 2

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