Question

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 1

Answer:

Step-by-step explanation:

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.