Please find the attachment for a better understanding of the solution provided here.
We have been asked to find the work done by a force F of 21 pounds acting in the direction <2,5> in moving an object 7 feet from (0,0) to (7,0).
As we can see clearly from the question above that the object moves exclusively in the direction of the x axis and thus, the component of the force acting is only the x component. So, our main aim will be to find the x component of the force. Once it is found we will simply multiply it with the distance travelled in the x axis to find the work done as asked in the question.
Let us call the x component of the force as [tex] F_{x} [/tex].
From the diagram in the attachment, we can see that the [tex] \angle BAC=\arctan(\frac{5}{2})=68.2 [/tex] degrees
Thus, [tex] F_{x}=21 cos(68.2)=7.799 [/tex]feet
[tex] F_{x}=54.593 [/tex]feet-pound
Thus, A is the correct option
