Respuesta :

sqdancefan

Triangle SET is similar to triangle SAR, so corresponding sides have the same ratio. This means

... ST : SR = ET : AR = 8.19 : 6.37

Then ST : TR = 8.19 : (6.37+8.19) = 8.19 : 14.56

Using division symbols, this is

... ST/TR = 8.19/14.56

Multiplying by TR gives

... ST = TR×(8.19/14.56) = 20.8×8.19/14.56

... ST = 11.7

check the picture below.


so, therefore, the triangles are similar by AA.


now, notice the length RT = 20.8, thus whatever ST might be, RS picks up the slack from the 20.8, namely RS = 20.8 - ST. Then we can use proportions from the corresponding sides.


[tex] \bf \cfrac{ET}{RA}=\cfrac{ST}{RS}\implies \cfrac{8.19}{6.37}=\cfrac{ST}{20.8-ST}\implies \stackrel{\textit{cross-multiplying}}{170.352-8.19ST=6.37ST}
\\\\\\
170.352=6.37ST+8.19ST\implies 170.352=14.56ST
\\\\\\
\cfrac{170.352}{14.56}=ST\implies 11.7=ST [/tex]

Ver imagen jdoe0001

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