8. ABCD is a parallelogram whose diagonals intersect each other at right angles. If
the length of the diagonals is 6 cm and 8 cm, find the lengths of all the sides of
the parallelogram.
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8. ABCD is a parallelogram whose diagonals intersect each other at right angles. If
the length of the diagonals is 6 cm and 8 cm, find the lengths of all the sides of
the parallelogram.
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Answer:
Given that ABCD is a parallelogram whose diagonals measure 6 cm and 8 cm respectively. Let the diagonals interest each other at point O.
Since we know that the diagonals of parallelogram bisect each other ,
AO=CO= 3 cm ( Since AC = 6 cm) and. BO=DO=4 cm ( since BD= 8 cm)
triangle AOB is right angled at O.
Applying Pythagoras theorem we get ,
AB² = OA²+ OB²
AB² = 6²+8²
AB²= 36+64
AB²= 100
AB =√100
AB = 10 cm
AB=BC=CD=AD= 10 cm