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Question

ABC is a triangle and M & N are points on AB and AC such that MN || BC. Find the given ratios if AM:MB = 2:3.


Your Answer
A
2:3
Your Answer
B
2:5
Your Answer
C
3:5

Solution

The correct option is

According to BPT, if a line is drawn parallel to one side of a triangle to intersect the other two sides in different points then the other two sides are divided in the same ratio.

AMMB=ANNC


Given AM:MB=2:3AN:NC=2:3

ANNC=23
Adding one on both sides, we get,

ANNC+1=23+1

AN+NCNC=2+33

ACNC=53

NC:AC=3:5

NCAN=32
Adding one on both sides, we get,

NCAN+1=32+1

NC+ANAN=3+22

ACAN=52

AN:AC=2:5

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