A) \[{{d}_{1}}=215.04\,m;\,{{d}_{2}}=96.25\,m\]
B) \[{{d}_{1}}=110.15\,m;\,{{d}_{2}}=26.15\,m\]
C) \[{{d}_{1}}=96.15\,m;\,{{d}_{2}}=42.16\,m\]
D) \[{{d}_{1}}=145.83\,m;\,{{d}_{2}}=65.83\,m\]
Correct Answer: D
Solution :
Here, the area of rhombus\[=A=4800\,{{m}^{2}}\] Side of rhombus\[=a=40\,m\] One diagonal, \[{{d}_{1}}=?\] Second diagonal, \[{{d}_{2}}=?\] Using the correlation formula, \[{{({{d}_{1}}+{{d}_{2}})}^{2}}=4\,({{a}^{2}}+A)\]and \[{{({{d}_{1}}-{{d}_{2}})}^{2}}=4\,({{a}^{2}}-A)\] \[\Rightarrow {{({{d}_{1}}+{{d}_{2}})}^{2}}=4[{{(80)}^{2}}+4800]\] \[\Rightarrow {{d}_{1}}+{{d}_{2}}=2\sqrt{6400+4800}\] ?(i) \[\Rightarrow {{d}_{1}}+{{d}_{2}}=212.6\] Similarly, \[{{({{d}_{1}}-{{d}_{2}})}^{2}}=4\,[{{(80)}^{2}}-4800]\] \[\Rightarrow {{d}_{1}}+{{d}_{2}}=2\sqrt{1600}\] ?(ii) \[\Rightarrow {{d}_{1}}+{{d}_{2}}=80\] Solving (i) and (ii), \[{{d}_{1}}=145.83\,m;\,\,{{d}_{2}}=65.83\,m\]
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