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

solution

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.