Question

the perimeter of a rhombus is 2p units some of length of diagonal is m unit.then the area of rhombus is?​

Answer 1

Answer:

1/4(m^2−P^2)

Step-by-step explanation:

Side of Rhombus

=perimeter/4

=2P/4=P/2

Let, AC=2a

∴OA=OC=a

BD=2b

OB=OD=b

In Right △OBC,

a^2+b^2=p^2/4

4a^2+4b^2=P^2.....(i)

Also, 2a+2b=m

by squaring,

4a^2+ab^2+8ab=m^2

4a^2+4b^2=m^2−8ab.....(ii)

from (i) and (ii)

m^2−8ab=P^2

8ab=m^2−P^2

4×(2ab)=m^2−P^2

2ab=1/4(m^2−P^2)

Area of Rhombus

=> 1/2×d_1×d_2 = 1/2×2a×2b

=> 2ab = 1/4(m^2−P^2)