17. Answer: e) the correct answer is not provided
Step-by-step explanation:
It is easier to see which sides line up with each other if you write them under each other (at least that's what works for me):
[tex]\stackrel{STU}{SKL}\quad \rightarrow \quad \dfrac{ST}{SK}=\dfrac{TU}{KL}=\dfrac{SU}{SL}[/tex]
Set up a proportion for the sides that have measurements:
[tex]\dfrac{ST}{SK}=\dfrac{SU}{SL}\\\\\\\dfrac{143}{33}=\dfrac{12x+8}{24}\\\\\\143(24)=33(12x+8)\quad cross\ multiplied\\\\104=12x+8\qquad divided\ both\ sides\ by\ 33\\\\96=12x\qquad subtracted\ 8\ from\ both\ sides\\\\\boxed{8=x}\qquad divided\ both\ sides\ by\ 12[/tex]
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18. Answer: f) 9
Step-by-step explanation:
[tex]\stackrel{HGF}{HKL}\quad \rightarrow \quad \dfrac{HG}{HK}=\dfrac{GF}{KL}=\dfrac{HF}{HL}\\\\\\\dfrac{HG}{HK}=\dfrac{HF}{HL}\\\\\\\dfrac{35}{14}=\dfrac{5x+5}{20}\\\\\\35(20)=14(5x+5)\qquad cross\ multiplied\\\\50=5x+5\qquad divided\ both\ sides\ by\ 14\\\\10=x+1\qquad divided\ both\ sides\ by\ 5\\\\\boxed{9=x}\qquad subtracted\ 1\ from\ both\ sides[/tex]
