a) The value of y is 75 / 13, b) The measures of line segments RS and ST are 639 / 13 and 466 / 13.
What are the values of y and the lengths of the line segments RS and ST?
a) In this problem we have a geometric system generated by two collinear line segments. First, we need to solve for y in the following expression:
RT = RS + ST
85 = 8 · y + 3 + 5 · y + 7
85 = 13 · y + 10
13 · y = 75
y = 75 / 13
b) Finally, we evaluate the expressions of RS and ST for y:
RS = 8 · y + 3
RS = 8 · (75 / 13) + 3
RS = 639 / 13
ST = 5 · (75 / 13) + 7
ST = 466 / 13
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