A) \[\sqrt{2}:1\]
B) \[\sqrt{3}:1\]
C) \[2:1\]
D) \[1:3\]
Correct Answer: D
Solution :
Here \[{{m}_{1}}+{{m}_{2}}=\frac{-2h}{b}\] .....(i) and \[{{m}_{1}}{{m}_{2}}=\frac{a}{b}\] .....(ii) Also, given that \[4ab=3{{h}^{2}}.\]Now we have to find \[\frac{{{m}_{1}}}{{{m}_{2}}}\], therefore with the help of (i) and (ii), we get \[{{({{m}_{1}}-{{m}_{2}})}^{2}}=\frac{4{{h}^{2}}-4ab}{{{b}^{2}}}=\frac{4{{h}^{2}}-3{{h}^{2}}}{{{b}^{2}}}=\frac{{{h}^{2}}}{{{b}^{2}}}\] Þ \[{{m}_{1}}-{{m}_{2}}=\frac{h}{b}\] .....(iii) Now on solving (i) and (iii), we get \[{{m}_{1}}=\frac{-h}{2b}\]and \[{{m}_{2}}=\frac{-3h}{2b}\]; \\[{{m}_{1}}:{{m}_{2}}=1:3\].
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