Question

$ABCD$ is a parallelogram whose diagonals intersect each other at right angles. If the length of the diagonals is $6cm$ and $8cm$, find the lengths of all the sides of the parallelogram.

Answer 1

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

=> = AB

=> 5 = AB

So, AB = 5cm

AB = BC = CD = AD (all sides of rhombus are equal)

Each side of the parallelogram ABCD is 5cm.