All the sides of the rhombus are equal.
The area of a rhombus is
(d1).(d2)=12 d1×d2=24 The length of the side of a rhombus is given by
. This is because the two diagonals and a side from a right-angled triangle with sides
, and the side length.
=5 Hence,
√d12+d22=10 d12+d22=100 Using
d1×d2=24,2×d1×d2=48 d12+d22+2.d1.d2=100+48=148 d12+d22−2.d1.d2=100−48=52 d1+d2=√148...(1)
d1−d2=√52...(2)
adding equation (1) and (2), we get,
2×d1=2×(√37+√13) d1=√37+√13 or
In a rhombus the area of a Rhombus is given by :
The diagonals perpendicularly bisect each other. Considering the length of the diagonal to be 2a, 2b.
The area of a Rhombus is :
.(2a).(2b)=12 ab=6 .
The length of each side is :
√a2+b2=5,a2+b2=25 (a+b)2=37,(a+b)=√37 (a−b)2=13,(a−b)=√13 2a=(√37+√13) ,
2b=(√37−√13) 2a is longer diagonal which is equal to
√37+√13