A) 12.5
B) 13
C) 13.2
D) 12
Correct Answer: D
Solution :
\[\cos 60\,=\frac{4+25\,-{{c}^{2}}}{2.2.5}\] \[10=29-{{c}^{2}}\] \[{{c}^{2}}=19\] \[\] \[-\frac{1}{2}\,=\frac{{{a}^{2}}+{{b}^{2}}-19}{2ab}\] \[{{a}^{2}}+{{b}^{2}}-19=-ab\] \[{{a}^{2}}+{{b}^{2}}+ab=19\] Area \[=\frac{1}{2}\,\times 2\times 5\,\sin 60\,+\frac{1}{2}\,ab\,\sin x\,=4\sqrt{3}\] \[\frac{5\sqrt{3}}{2}\,+\frac{ab\sqrt{3}}{4}\,=4\sqrt{3}\] \[\frac{ab}{4}\,=4-\frac{5}{2}=\frac{3}{2}\] \[\] \[{{a}^{2}}+{{b}^{2}}=13\] \[\] Perimeter \[=2+5+2+3\] \[=12\]You need to login to perform this action.
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