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In the figure, PQ is parallel to RS. The length of RP is 5 cm; the length of PT is 30 cm; the length of QT is 60 cm. what is the length of SQ? A. 10 cmB. 2 cmC. 6 cmD. 20 cmme and my sister are trying to do this, and we really can't figure out what the side lengths are. help would be very appreciated!

In the figure PQ is parallel to RS The length of RP is 5 cm the length of PT is 30 cm the length of QT is 60 cm what is the length of SQ A 10 cmB 2 cmC 6 cmD 20 class=

Respuesta :

Looking at the given diagram,

PQ is parallel to RS

This means that

Triangle PQT is similar to triangle RST

We can say that

PT/RT = QT/ST

Given that

PT = 30 cm, QT = 60 cm

RP = 5 cm

RT = RP + PT = 5 + 30

RT = 35 cm

ST = QT + SQ = 60 + SQ

Therefore,

30/35 = 60/(60 + SQ)

By cross multiplying, it becomes

30(60 + SQ) = 35 * 60

1800 + 30SQ = 2100

30SQ = 2100 - 1800

30SQ = 300

SQ = 300/30

SQ = 10 cm

OPtion A is Correct

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