Answer:
s = 12
Explanation:
Corresponding sides of similar triangles are proportional. For similar triangles ABC and XYZ, pairs of corresponding sides are ...
AB and XY . . . . 6 and 9
BC and YZ . . . . not given
CA and ZX . . . . 8 and S
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We can write the statement of proportionality four (4) different ways. For purposes of finding the unknown S, it is convenient to choose an equation that has S in the numerator:
ZX/CA = XY/AB
S/8 = 9/6
Multiplying by 8 gives the value of S:
S = 8(9/6)
S = 12
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Additional comment
Other ways we could write the statement of proportionality are ...
CA/ZX = AB/XY ⇔ 8/S = 6/9
ZX/XY = CA/AB ⇔ S/9 = 8/6
XY/ZX = AB/CA ⇔ 9/S = 6/8