The triangles are similar. If PN = 12, QP = 8, and PM = 17, find QR.

Mathematics

1 answer:

natulia [17]2 years ago

3 0

Answer:

28 1/3

Step-by-step explanation:

Corresponding sides of similar triangles are proportional.

<h3>setup</h3>

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

<h3>solution</h3>

QR = 17(20/12) = 28 1/3 . . . . . multiply by 17

The length of QR is 28 1/3 units.
_____

<em>Additional comment</em>

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.

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Step-by-step explanation:

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