we have that
In a rhombus the length sides are congruent
the diagonals bisect each other and are perpendicular
so
If mmIn the right triangle IFJ
mtan(30)=FJ/IJ
Remember that
[tex]\tan (30^o)=\frac{\sqrt[]{3}}{3}[/tex]
FJ=4
substitute the given values
[tex]\begin{gathered} \frac{\sqrt[]{3}}{3}=\frac{4}{IJ} \\ \\ IJ=\frac{12}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=4\sqrt[]{3} \end{gathered}[/tex]
Find the length side IF
Applying Pythagorean Theorem
IF^2=4^2+IJ^2
IJ^2=48
IF^2=16+48
IF^2=64
IF=8 units
that means
side GH=8 units
side JG=side IJ=4√3 units
side FH=2*side FJ=2*4=8 units
