Finding the resultant couple moment

[theBEAST]

Homework Statement

I attached the question as a picture to this thread

Homework Equations

M=Fd

The Attempt at a Solution

I was taught that the moment produced by two equal but opposite forces is the magnitude of one force multiplied by the distance between the two forces.

I used Pythagoras to solve for the distances between each of the couples and found sqrt32 and sqrt8 to be these distances.

Thus
M1= 150*sqrt32
M2=200*sqrt8

and the resultant moment
=M1-M2
=283Nm [clockwise]

This is not the answer, the method the answer key used was breaking up the couples into x and y. I don't understand why my method does not work as well.

 

[tiny-tim]

hi theBEAST!

… the distances between each of the couples and found sqrt32 and sqrt8 to be these distances.

nooo …

√32 and √8 are the distances between the points of application of these forces

the couple uses the distance between the lines of application of the forces