Question

Find x and y so the quadrilateral is a parallelogram

Answer 1

Result

• x = 7

• y = 4

Explanation:

Given the parallelogram

Here are some of the properties of a parallelogram:

• The opposite sides of a parallelogram are equal.

• The opposite angles of a parallelogram are equal.

• The diagonals of a parallelogram bisect each other.

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

In our case, the diagonals PR and QS bisect each other.

Thus, we get

• RT = TP

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

`x = 5x-28`

`5x-x = 28`

`4x = 28`

divide boh sides by 4

`4x/4 = 28/4`

`x = 7`

• Therefore, the value of x = 7

Similarly, we can determine the value of y.

As

`QT = TS`

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

`5y = 2y+12`

`5y-2y = 12`

`3y = 12`

divide both sides by 3

`3y/3 = 12/3`

`y = 4`

• Therefore, the value of y = 4

Result

• x = 7

• y = 4