Question

Geometry special parallelogramsSide GH =Side JG =Side FH =

Answer 1

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

`\tan (30^o)=\frac{\sqrt[]{3}}{3}`

FJ=4

substitute the given values

`\begin{gathered} \frac{\sqrt[]{3}}{3}=(4)/(IJ) \\ \\ IJ=\frac{12}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=4\sqrt[]{3} \end{gathered}`

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