Question

Solve for x. The triangles in each pair are similar.

Answer 1

17. Answer: e) the correct answer is not provided

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):

`\stackrel{STU}{SKL}\quad \rightarrow \quad (ST)/(SK)=(TU)/(KL)=(SU)/(SL)`

Set up a proportion for the sides that have measurements:

`(ST)/(SK)=(SU)/(SL)\\\\\\(143)/(33)=(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`

**************************************************************************************

18. Answer: f) 9

Explanation:

`\stackrel{HGF}{HKL}\quad \rightarrow \quad (HG)/(HK)=(GF)/(KL)=(HF)/(HL)\\\\\\(HG)/(HK)=(HF)/(HL)\\\\\\(35)/(14)=(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`