Answer:
28 1/3
Explanation:
Corresponding sides of similar triangles are proportional.
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setup
Triangle NPM is similar to triangle NQR, so the proportion of interest is ...
QR/PM = QN/PN . . . . . ratios of corresponding sides
Filling in the given values, we have ...
QR/17 = (8 +12)/12 . . . . . . . . QN = QP+PN
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solution
QR = 17(20/12) = 28 1/3 . . . . . multiply by 17
The length of QR is 28 1/3 units.
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Additional comment
Corresponding vertices are listed in the same order in the similarity statement. Corresponding segments can be found by considering the position of the endpoint vertices in the similarity statement.
It is generally convenient to write the proportion with the unknown length in the numerator. This means the equation can be solved by simply multiplying by that denominator.