A) \[4\sqrt{30}\,c{{m}^{2}}\]
B) \[8\sqrt{30}\,c{{m}^{2}}\]
C) \[6\sqrt{30}\,c{{m}^{2}}\]
D) \[5\sqrt{30}\,c{{m}^{2}}\]
Correct Answer: B
Solution :
Let a, b and c be the three sides of \[\Delta ABC.\] Given \[a=11\,cm\]and \[a+b+c=32\,cm\] \[\Rightarrow \]\[11+b+c=32\,cm\] \[\Rightarrow \]\[b+c=21\,cm\] ?(i) Also, we are given that \[b-c=5\,cm\] ?(ii) Adding (i) and (ii), \[2b=26\,cm\] \[\Rightarrow \]\[b=13\,cm\]and \[c=8\,cm\] Now, \[s=\frac{a+b+c}{2}=\frac{32}{2}=16\,cm\] Area of \[\Delta ABC=\sqrt{s(s-a)(s-b)(s-c)}\] \[=\sqrt{16\times (16-11)\times (16-13)\times (16-8)}\] \[=\sqrt{16\times 5\times 3\times 8}=\sqrt{64\times 30}=8\sqrt{30}\,c{{m}^{2}}\]
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