Question

the diognals of a parallelogram intersect at right angles.IF The length of diognals is 6cm and 8cm,find the lenght of all sides of parallelogram

Answer 1

Let AC and BD are the diagonal of the parallelogram.

Here, AC = 12 cm, BD = 16 cm

Now, AC and BD bisect each other ate right angle at the point O.

Now, OB = BD/2 = 16/2 = 8

OA = AC/2 = 12/2 = 6

and ∠AOB = 90

From triangle AOB

Using Pytahgorus Theorem,

      AB2 = OB2 + OA2

=> AB2 = 82 + 62

=> AB2 = 64 + 36

=> AB2 = 100

=> AB = √100

=> AB = 10 cm

Similarly, From triangle COB, COD and AOD,

the length of BC, CD, and AD is equal to 10 cm each.

Now, perimeter  = 2(10 + 10) = 2*20 = 40 cm

Answer 2

Let AC and BD are the diagonal of the parallelogram.

Here, AC = 6 cm, BD = 8 cm

Now, AC and BD bisect each other ate right angle at the point O.

Now, OB = BD/2 = 8/2 = 4

OA = AC/2 = 6/2 = 3

and ∠AOB = 90

From triangle AOB

Using Pytahgorus Theorem,

      AB2 = OB2 + OA2

=> AB2 = 32 + 42

=> AB2 = 9 + 16

=> AB2 = 25

=> AB = √25

=> AB = 5 cm

Similarly, From triangle COB, COD and AOD,

the length of BC, CD, and AD is equal to 5 cm each