Question

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!

Answer 1

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