Question

Find the area of a rhombus whose perimeter is 200 m and one diagonal are

80 m.​

Answer 1

Step-by-step explanation:

LEt a be the side of the rhombus

It is given that perimeter of the rhombus =200m

⇒ 4a=200

⇒ a=

4

200

=50m

One diagonal of rhombus d

1

=80m, Let d

2

be the second diagonal

We know that diagonals of a rhombus are perpendicular bisectors

∴(

2

80

)

2

+(

2

d

2

)

2

=a

2

(40)

2

+

4

d

2

2

=50

2

⇒

4

d

2

2

=2500−1600⇒d

2

2

=4.900⇒d

2

2

=3600⇒d

2

=60m

Area of the rhombus =

2

d

1

d

2

=

2

80×60

=2400m

2