Question

A quadrilateral ABCD :

AB = CD = 4
BC = x + 8
AD = 3x - 2

For what value of x is this quadrilateral a parallelogram?

Answer 1

Hello !

A parallelogram has its opposite sides equal.

So BC must be equal to AD (AB and CD are already equal)

`x + 8 = 3x - 2\\\\8 + 2 = 3x - x\\\\10 = 2x\\\\x = 10/2\\\\\boxed{x = 5}`

If x = 5, the quadrilateral ABCD is a parallelogram.

Answer 2

Properties of parallelogram :

1. Opposite sides are equal.
2. Opposite sides are parallel
3. Opposite angles add upto 180°
4. Opposite angles are also equal.

As per question AB and CD are opposite sides.

Since AB and CD are equal sides So, BC and AD must be equal.

AD = BC

`\sf 3x - 2 = x + 8`

`\sf 3x - x = 8 + 2`

`\sf 2x = 10`

`\sf x = (10)/(2)`

`{\boxed{\sf {x = 5 }}}`

BC = x + 8 = 5 + 8 = 13

AD = 3x -2 = 3(5)- 2 = 15 - 2 = 13

In conclude we get BC and AD are equal sides.

Therefore for x = 5 the given quadrilateral ABCD is a parallelogram.