Question

Solve for variables. SHOW WORK PLEASE.

Answer 1

f = 4 and g = 20

Explanation:

Whole triangle and small triangle are similar. Therefore the sides are in proportion:

`(3f-8+6)/(6)=(f+2+9)/(9)\\\\(3f-2)/(6)=(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`

We have second proportion:

`(g)/(4+6)=(12)/(6)\\\\(g)/(10)=2\qquad\text{multiply both sides by 10}\\\\\boxed{g=20}`