Question

In the figure, PQ is parallel to RS . The length of RP is 7 cm; the length of PT is 35 cm; the length of SQ is 13 cm. What is the length of QT ?

Answer 1

The answer will be 65, as the line PQ is parallel to RS so the ratio of TP and PR will be same as the ratio of TQ and QS.

Answer 2

Answer: Option B. is the right answer.The length of QT is 65 cm.

Step-by-step explanation:

Given:In ΔRST ,PQ is a line parallel to RS and dividing RT and ST in same ratio(by Basic proportionality theorem)

$\frac{PT}{RP}=\frac{QT}{SQ}\\\\\text{by putting the given values of RP=7 ,PT=35 and SQ=13 ,we get}\\\\\frac{35}{7}=\frac{QT}{13}\\\\\Rightarrow5=\frac{QT}{13}\\\\\Rightarrow\ QT=5\times13=65\ cm$

Basic Proportionality theorem states that if a line is drawn parallel to one side of a triangle to intersect the other two side in distinct points, the other two sides are divided in the same ratio.

Therefore, the length of QT is 65 cm.