If l is inversely proportional to square root of m and l = 6 when m = 4 . What is the value of m when l = 4 ?

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Please find below the solution to the asked query :

$$\begin{gathered} \mathrm{As} \mathrm{I} \mathrm{is} \mathrm{inversely} \mathrm{proportional} \mathrm{to} \mathrm{square} \mathrm{root} \mathrm{of} \mathrm{m}. \\ \mathrm{So}, \\ \mathrm{I} =\frac{\mathrm{k}}{\sqrt{\mathrm{m}}} , \mathrm{where} \mathrm{k} \mathrm{is} \mathrm{a} \mathrm{proportionality} \mathrm{constant} \\ \mathrm{l}=6 , \mathrm{when} \mathrm{m}=4 \\ \mathrm{So}, \\ 6=\frac{\mathrm{k}}{\sqrt{4}} \\ 6=\frac{\mathrm{k}}{2} \\ \mathrm{k}=12 \\ \mathrm{Now}, \\ \mathrm{l}=\frac{12}{\sqrt{\mathrm{m}}} \\ \mathrm{when} \mathrm{l}=4 \\ 4=\frac{12}{\sqrt{\mathrm{m}}} \\ \sqrt{\mathrm{m}}=3 \\ \mathrm{Squaring} \mathrm{on} \mathrm{both} \mathrm{sides}, \mathrm{we} \mathrm{get} \\ \mathrm{m}=9 \mathrm{ANS}... \end{gathered}$$

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