Question:
ABCD is a parallelogram whose diagonals intersects each other at right angles if the length of the diagonals are 16 centimetre and 12 centimetre find the length of all sides and its perimeter
Answer:
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
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