A) \[a({{m}_{1}}-{{m}_{2}})\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}+4}\]
B) \[({{m}_{1}}-{{m}_{2}})\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}+4}\]
C) \[a({{m}_{1}}-{{m}_{2}})\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}-4}\]
D) \[({{m}_{1}}-{{m}_{2}})\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}-4}\]
Correct Answer: A
Solution :
\[s=\sqrt{{{(am_{1}^{2}-am_{2}^{2})}^{2}}+{{(2a{{m}_{1}}-2a{{m}_{2}})}^{2}}}\] \[=\,a\,({{m}_{1}}-{{m}_{2}})\,\,\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}+4}\].
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