The length of FH is 23.
In triangle FGH, given that GJ is an angle bisector of angle G and is perpendicular to FH, we have a right-angled triangle GJF with a right angle at J and GJ perpendicular to FH.
Additionally, GJH is another right-angled triangle formed by the perpendicular GJ and side GH.
The triangles GJF and GJH are congruent by the ASA (Angle-Side-Angle) criterion.
Given that GF = 2x + 3 and GH = 23, we know that GJF and GJH are congruent, and their corresponding sides are equal.
Therefore:
2x + 3 = 23
Solving for x:
2x = 20
x = 10
Now, substitute x = 10 back into the expression for FH:
FH = 2x + 3 = 2(10) + 3 = 20 + 3 = 23
Therefore, the correct answer for the length of FH is:
FH = 23
So, the correct option is C. 23.
The probable question may be:
In triangle FGH, GJ is an angle bisector of G and perpendicular to FH.
GF=2x+3 and GH=23, angle GJF=angle GJH=90 degree
triangle GJF & GJH are congruent by ASA so 2x+3=23. What is the length of FH? O A. 13 OB. 10 OC. 23 O D.20