Question

What is the length of side AB of parallelogram ABCD? units?

Answer 1

SOLUTION:-

□ ABCD is a parallelogram.

•°• opposite sides are congruent

•°• AB = DC

=> 4q - 8 = q + 4

=> 4q - q = 4 + 8

=> 3q = 12

=> q = 12/3 = 4

=> q = 4

now

Length of side AB = 4q - 8

= 4 × 4 - 8

= 16 - 8

= 8

The length of side AB is 8 unit.

More properties of parallelogram:-

Opposite sides of a parallelogram are congruent.

Opposite angles of a parallelogram are congruent.

Consecutive angles of a parallelogram are supplementary.

If a parallelogram has 1 right angle, then it has 4 right angles.

The diagonals of a parallelogram bisect each other.

Answer 2

$\sf{\underline{\boxed{\mathfrak{Given}}}}$

• ABCD is a parallelogram
• DC = q + 4
• AB = 4q - 8

$\sf{\underline{\boxed{\mathfrak{To\:find}}}}$

• AB = ????

$\sf{\underline{\boxed{\mathfrak{Solution}}}}$

☆ opposite sides of the parallelogram are equal .

➪Therefore ; AB = DC

➦4q - 8 = q + 4

➦4q - q = 8 + 4

➦3q = 12

➦q = 12 / 3

➦q = 4

☆putting value of x

➦AB = 4q - 8

➦AB = 4 x 4 - 8

➦AB = 16 - 8

➦AB = 8 units

$\sf{\bold{\underline{\boxed{ AB \: = \: 8 units}}}}$

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