Question

In the figure, PQ is parallel to RS. The legth of RP is 4 cm; the length of PT is 16 cm; the length of QT is 20 cm. What is the length of SQ?

Answer 1

In the figure, PQ is parallel to RS, then

• ∠TPQ≅∠TRS (as corresponding angles);
• ∠TQP≅∠TSR (as corresponding angles).

Consider triangles TPQ and TRS. These triangles are similar by AAA theorem, because

• ∠TPQ≅∠TRS (as corresponding angles);
• ∠TQP≅∠TSR (as corresponding angles);
• ∠T is common.

Then

`(TP)/(TR)=(TQ)/(TS).`

If PR = 4 cm and PT = 16 cm, then TR = TP + PR = 16 + 4 = 20 cm.

Thus,

`(16)/(20)=(20)/(TS)\Rightarrow TS=(20\cdot 20)/(16)=25\ cm.`

Note that TQ + QS = TS, then QS = TS - TQ = 25 - 20 = 5 cm.

Answer: correct choice is A

Answer 2

RP/PT=SQ/QT
4/16=SQ/20
SQ=5