Question

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 length of all sides of parallelogram.

Answer 1

half of 1st diagonal=3cm
half of 2nd diagonal=4cm
one side of ∥gm=√[3²+4²]=5cm
other side of ∥gm also=5cm
so it is square with each side = 5cm
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Answer 2

ABCD is a parallelogram whose diagonals intersect each other at O with 90°.
so it's a rhombus as diagonals of rhombus interest each other at right angles.

diagonal1 (AC) = 6cm
diagonal 2(BD) = 8cm

OD = OB = 3cm each
OA = OC = 4cm each

Let, us take triangle AOB
it is a right angled triangle

=> (OA)² + (OB)² = (AB)²

=> (4)² + (3)² = (AB)²

=> 16 + 9 = (AB)²

=> 25 = (AB)²

=> $\sqrt{25}$ = AB

=> 5 = AB

So, AB = 5cm
AB = BC = CD = AD (all sides of rhombus are equal)

Each side of the parallelogram ABCD is 5cm.