Question

ABCD is a parallelogram the diagonals of the parallelogram intersect at O

Answer 1

Answer:

Each side of the parallelogram ABCD is 5cm.

Step-by-step explanation:

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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.

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Solution

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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.