we have that
GE=46
DH=15
GF=?
we know that
the rhombus has two perpendicular diagonals
and
GE=GH+HE
GH=HE
DF=DH+HF
DH=HF
so
GE=46------------> GH=46/2------------> GH=23
DH=15-------------> HF=15
so
applying the Pythagorean theorem
GF²=GH²+HF²----------> 23²+15²----------> 754
GF=√754----------> GF=27.46 in
the answer is
GF=27.46 in
