Answer:
[tex] ST = 12 [/tex]
Step-by-step explanation:
By AA Similarity, triangles ASR and EST are similar.
The ratio of the lengths of the sides of triangle ASR to those of EST is 6/8 or 3/4.
[tex] \dfrac{SR}{ST} = \dfrac{3}{4} [/tex]
Also,
[tex] SR + ST = 21 [/tex]
By a rule of proportions, you get
[tex] \dfrac{SR + ST}{ST} = \dfrac{3 + 4}{4} [/tex]
[tex] \dfrac{21}{ST} = \dfrac{7}{4} [/tex]
[tex] 7ST = 4 \times 21 [/tex]
[tex] 7ST = 84 [/tex]
[tex] ST = 12 [/tex]
