A) \[~9100\,{{m}^{2~}}\]
B) \[~9000\,{{m}^{2}}\]
C) \[~9200\,{{m}^{2}}\]
D) \[~9500\,{{m}^{2}}\]
Correct Answer: B
Solution :
Let the sides of the triangle be \[a=25x,\,b=17x,\,c=12x\] Perimeter of triangle = 540cm \[\Rightarrow \]\[25x+17x+12x=540\] \[\Rightarrow \]\[54x+540\Rightarrow x=10\] \[\therefore \]\[a=25\times 10=250m,\,b=17\times 10=170\,m,\] \[c=12\times 10=120\,m.\] Now, \[s=\frac{540}{2}=270\,m\] \[\therefore \] Area of triangle \[=\sqrt{270(270-250)(270-170)(270-120)}\] \[=\sqrt{270\times 20\times 100\times 150}\,{{m}^{2}}=9000\,{{m}^{2}}.\]
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