Question

Find x and y so the quadrilateral is a parallelogram.

Answer 1

Summary:

• The value of x = 7

• The value of y = 4

Explanation:

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

As

The parallelogram PQRS is given, so

RT = TP

Given

• RT = x

• TP = 5x-28

plug in RT = x and TP = 5x-28 in the equation RT = TP

RT = TP

x = 5x-28

switch the sides

5x-28 = x

adding 28 in both sides

5x-28+28 = x+28

simplify

5x = x+28

subtract x from both sides

5x-x = x+28-x

4x = 28

divide boh sides by 4

4x ÷ 4 = 28 ÷ 4

simplify

x = 7

Therefore, we conclude that the value of x is: x = 7

Similarly,

QT = TS

Given

• QT = 5y

• TS = 2y+12

plug in QT = 5y and TS = 2y+12 in the equation QT = TS

QT = TS

5y = 2y+12

subtract 2y from both sides

5y - 2y = 2y+12-2y

simplify

3y = 12

divide both sides by 3

3y ÷ 3 = 12 ÷ 3

simplify

y = 4

Therefore, we conclude that the value of y is: y = 7

Summary:

• The value of x = 7

• The value of y = 4