Question

Given that the length of PR = 10 cm and SQ = 24 cm, what is the perimeter of the parallelogram PQRS? *

Answer 1

Answer:

Let ABCD be the rhombus where, AC=10cm and BD=24cm

Let AC and BD intersect each other at O.Now, diagonals of rhombus bisect each other at right angles.

Thus, we have

AO=

2

1

×AC=

2

1

×10=5cm and

BO=

2

1

×BD=

2

1

×24=12cm

In right angled △AOB,

⇒ (AB)

2

=(AO)

2

+(BO)

2

⇒ (AB)

2

=(5)

2

+(12)

2

⇒ (AB)

2

=25+144

⇒ (AB)

2

=169

∴ AB=13cm

∴ The length of each side of rhombus is 13cm