Answer:
The length of side FG is 19 units.
Step-by-step explanation:
Let the midpoint of FH be P.
In triangle FGP and triangle HGP,
[tex]FP=HP[/tex] (Given)
[tex]\angle FPG=\angle HPG=90^{\circ}[/tex] (Given)
[tex]PG=PG[/tex] (Common side)
By SAS postulate,
[tex]\triangle FGP\cong \triangle HGP[/tex]
Now,
[tex]FG=HG[/tex] (CPCTC)
[tex]5x-6=3x+4[/tex]
[tex]2x=10[/tex]
[tex]x=5[/tex]
The value of x is 5.
[tex]FG=5(5)-6=19[/tex]
Therefore the length of side FG is 19 units.
