Question

Point P on the side AB od triangle ABC splits AB so that AP:BP=1:3. If M is the midpoint of CP, then the ratio of the area of triangle BPM to the area of triangle ABC is

A)1/4
B)5/8
C)3/8
D)3/16

I know that the rule is if two triangles have cogruent sltitudes , then the ratio of their area is equal to the ratio of the sides to which those altitudes are draw,
so based on that therom i got C but when i went back to check on my work i got lost on why does this work
it souds so confusing it would be a GREAT help for me if you could explain thanks

Answer 1

I am sure you made a sketch
let triangel APC = x
then triangle PBC = 3x
the whole triangle ABC = 4x

Since M is the midpoint, triangle BPM = (1/2) of 3x
= 3x/2

ratio of ∆BPM : ∆ABC = 3x/2 : 4x
= 3/2 : 4
= 3 : 8

you had C, so correct

Answer 2

thanks