Answer:
[tex]FH=16\ units[/tex]
Step-by-step explanation:
we know that
An isosceles triangle has two equal sides and two equal interior angles
In this problem
Triangle FGH is an isosceles triangle,
because
[tex]m\angle FGJ=m\angle HGJ[/tex] ---> given problem
[tex]m\angle FJG=m\angle HJG[/tex] ---> given problem
so
[tex]m\angle GFH=m\angle GHF[/tex]
therefore
FG=HG
substitute the given values
[tex]3x-8=16[/tex]
solve for x
[tex]3x-8=16[/tex]
[tex]3x=16+8[/tex]
[tex]3x=24[/tex]
[tex]x=8[/tex]
GJ divide triangle FGH into two congruent triangles
FGJ≅HGJ
If two figures are congruent, then its corresponding sides and its corresponding angles are congruent
so
HJ=FJ
FH=2FJ
FH=2x
substitute the value of x
[tex]FH=2(8)=16\ units[/tex]
