Question

For what values of x and y is PQRS a parallelogram?

Answer 1

x = 3

y = 2

Explanation:

GIVEN :-

• PQ = 2y + 3
• QR = 4y + 1
• RS = y + 5
• PS = 4x - 3

TO FIND :-

• The values of x & y for which PQRS will be a parallelogram

FACTS TO KNOW BEFORE SOLVING :-

In a parallelogram , pair of opposite sides are always equal in length.

SOLUTION :-

PQRS will be a parallelogram only when :-

• PQ = RS
• and PS = QR

1) Assume that PQ = RS.

`=> 2y + 3 = y + 5`

`=> 2y - y = 5 - 3`

`=> y = 2`

∴ For y = 2 , PQ = RS.

2) Now, assume that PS = QR.

`=> 4x - 3 = 4y + 1`

(Put y = 2 in the equation)

`=> 4x - 3 = 4 * 2 + 1`

`=> 4x - 3 = 9`

`=> 4x = 9 + 3 = 12`

`=> x = (12)/(4) = 3`

∴ For x = 3 , PS = QR.

CONCLUSION :-

For x = 3 & y = 2 , PQRS is a parallelogram.