Answer:
f = 4 and g = 20
Step-by-step explanation:
Whole triangle and small triangle are similar. Therefore the sides are in proportion:
[tex]\dfrac{3f-8+6}{6}=\dfrac{f+2+9}{9}\\\\\dfrac{3f-2}{6}=\dfrac{f+11}{9}\qquad\text{cross multiply}\\\\9(3f-2)=6(f+11)\qquad\text{use distributive property}\\\\(9)(3f)+(9)(-2)=(6)(f)+(6)(11)\\\\27f-18=6f+66\qquad\text{add 18 to both sides}\\\\27f=6f+84\qquad\text{subtract 6f from both sides}\\\\21f=84\qquad\text{divide both sides by 21}\\\\\boxed{f=4}\\\\3f-8=3(4)-8=12-8=4[/tex]
We have second proportion:
[tex]\dfrac{g}{4+6}=\dfrac{12}{6}\\\\\dfrac{g}{10}=2\qquad\text{multiply both sides by 10}\\\\\boxed{g=20}[/tex]
