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(A) Given that the work done by both persons is equal: $W_A = W_B$.The formula for work done is $W = Fd \cos 	heta$.For person $A$: $W_A = F_A d \cos

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$2$

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(A) Given that the work done by both persons is equal: $W_A = W_B$.The formula for work done is $W = Fd \cos 	heta$.For person $A$: $W_A = F_A d \cos 45^{\circ}$.For person $B$: $W_B = F_B d \cos 60^{\circ}$.Equating the two: $F_A d \cos 45^{\circ} = F_B d \cos 60^{\circ}$.Substituting the values of $\cos 45^{\circ} = \frac{1}{\sqrt{2}}$ and $\cos 60^{\circ} = \frac{1}{2}$:$F_A 	imes \frac{1}{\sqrt{2}} = F_B 	imes \frac{1}{2}$.Rearranging for the ratio $\frac{F_A}{F_B}$:$\frac{F_A}{F_B} = \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{(\sqrt{2})^2} = \frac{1}{\sqrt{2}}$.Comparing this with $\frac{1}{\sqrt{x}}$,we get $x = 2$.

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