98. The length of a rectangle is given as $L \pm I$ and its width as $W \pm w$. (a) Show that the uncertainty in its area $A$ is $a=L w+l W$. Assume that the uncertainties $l$ and $w$ are small, so that the product $l w$ is very small and you can ignore it. (b) Show that the fractional uncertainty im the area is equal to the sum of the fractional uncertainty in length and the fractional uncertainty in width.

 98. The length of a rectangle is given as $L \pm I$ and its width as $W \pm w$. (a) Show that the uncertainty in its area $A$ is $a=L w+l W$. Assume that the uncertainties $l$ and $w$ are small, so that the product $l w$ is very small and you can ignore it. (b) Show that the fractional uncertainty im the area is equal to the sum of the fractional uncertainty in length and the fractional uncertainty in width. (c) A rectangular solid has dimensions $L \pm L, W \pm w$, and $H \pm h$. Find the fractional uncertainty in the volume, and show that it equals the sum of the fractional uncertainties in the length, width, and height.