Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal of the field and saved a distance equal to half the longer side. The ratio of the shorter side of the rectangle to the longer side is
\(l+b=\sqrt{l^{2}+b^{2}}+l / 2\) \[\] \(\frac{l}{2}+b=\sqrt{l^{2}+b^{2}}\) \[\] \(\frac{l^{2}}{4}+b^{2}+l b=l^{2}+b^{2}\) \[\] \(\frac{3}{4} l^{2}=l b \Rightarrow \frac{b}{l}=\frac{3}{4}\) \[\] Choice (D)\[\]
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