Question

Find x and y so the quadrilateral is a parallelogram.

Answer 1

We conclude that:

• The value of x = 7

• The value of y = 4

Explanation:

Given

• The parallelogram PQRS

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

so

`RT = TP`

Given

• RT = x

• TP = 5x-28

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

`RT = TP`

`x = 5x-28`

`5x = x+28`

`5x-x = 28`

`4x = 28`

divide both sides by 4

`4x/4 = 28/4`

`x = 7`

Therefore, the value of x:

• x = 7

Similarly,

`QT = TS`

Given

• QT = 5y

• TS = 2y+12

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

`QT = TS`

`5y = 2y+12`

`5y-2y = 12`

`3y = 12`

divide both sides by 3

`3y/3 = 12/3`

`y = 4`

Therefore, the value of y:

y = 4

Therefore, we conclude that:

• The value of x = 7

• The value of y = 4