Question

Perimeter of a rhombus is to be unit and sum of length of diagonal is $M$ unit, then area of rhombus is

Answer 1

side $=\frac{2P}{4}=\frac{P}{2}$

Let $AC=2a$

$\therefore OA=OC=a$

Similarly $OB=OD=b$

In $△OBC,a^2+b^2=\frac{P^2}{4}$

$⟹4a^2+4b^2=P^2$

$M=2a+2b$

$M^2=4a^2+4b^2+8ab$

$M^2-P^2=8ab$

Area $=\frac{1}{2}\times d_1\times d_2=2ab=\frac{1}{4}(M^2-P^2)$