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

x = 6, y = 8

Explanation:

The diagonals of a parallelogram bisect each other.
`(PT)/(QT)` ≅
`(TR)/(ST)`

• Set up a system of linear equations by substituting the algebraic expressions for each segment length.
  `(2x)/(x+2 )` ≅
  `(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