$$Diagonal\ of\ rec\tan gle\ =\sqrt{l^2+w^2}=8$$
Square both sides, we have
$$\left(\sqrt{l^2+w^2}\right)^2=8^2$$
$$l^2+w^2=8^2$$
$$Sum\ of\ the\ lengths\ of\ the\ sides=10$$
$$\left(l+w\right)=10$$
$$Note\ that\ the\ area\ of\ a\ rec\tan gle\ is\ equal\ to\ l\cdot w$$
$$So,\ Area=l\cdot w$$
$$\left(l+w\right)^2=\left(l^2+w^2\right)+2lw$$
$$\left(10\right)^2=\left(8^2\right)+2lw$$
$$100-64=2lw$$
$$lw=\frac{36}{2}=18\ \ \ \ \ \ \ \ \left(Option\ A\right)$$