In a triangle ABC, P and Q are two points on AB and AC, respectively, such that PQ parallel to BC. If AC = 5QC, then the ratio PQ : BC is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 4 : 5.
We know that,
By basic proportionality theorem, if a line is drwan parallel to one side of a traiangle it divides the other two sides proportionally thus,
⇒ AP/AB = AQ/AC = PQ/BC
given: AC = 5QC
⇒ AC = QC + AQ
⇒ AQ = AC - QC = 5QC - QC = 4QC
So,
⇒ AQ/AC = 4QC/5QC
⇒ AQ/AC = 4/5
Thus, AQ/AC = PQ/BC = 4/5