What is the Resultant of Four Proportional Forces on a Quadrilateral?

[batballbat]

Homework Statement

Four forces act along and are proportional to the sides of the quadrilateral ABCD, three act in the direction AB,BC and CD and the fourth acts from A to D; find the magnitude and direction of their resultant, and determine the point In which it meets CD.

The Attempt at a Solution

i summed up the vectors and its AD then it meets CD at D but its a wrong solution according to my book

 

[tiny-tim]

hi batballbat!

hint: the resultant of AB and BC must go through B, mustn't it?

 

[batballbat]

there is a different answer in the book but not a complete solution. and i don't know how to come up with such a solution

 

[tiny-tim]

(just got up :zzz: …)

what is the answer?

maybe you can work backwards from that? ​

 

[batballbat]

solution:
through B draw BL, parallel to AC, to meet CD in L; bisect DL in X; the resultatnt is a force through X, parallel to AD, and equal to twice AD.

 

[tiny-tim]

yes, that's what i have

ok, can you see that that the resultant of the forces AB and BC must lie along the line BL ?

 

[batballbat]

yes
please give a full solution

 

[tiny-tim]

please give a full solution

what??

read the forum rules again

now explain why the resultant of the forces AB and BC must lie along the line BL

 

[batballbat]

because the two forces are acting on B and the resultant of AB and BC acts along BL by parallelogram law

 

[tiny-tim]

because the two forces are acting on B and the resultant of AB and BC acts along BL by parallelogram law

that's correct

ok, now you need to combine that resultant (along BL) with the force CD …

which point must that go through?

 

[batballbat]

that i do not know and i guess that's what's troubling me.
should i translate the vector CD?
ALso the resultant acts along BL but is not equal to BL isn't it?

 

[batballbat]

resultant acts along AD