A) \[\frac{5}{2}(13+5\sqrt{3})sq.cm\]
B) \[\frac{5}{2}(8+5\sqrt{3})sq.cm\]
C) \[\frac{5}{2}(10+5\sqrt{3})sq.cm\]
D) 30cm
Correct Answer: C
Solution :
By Heron's formula, we have area of triangle \[{{\text{l}}^{2}}={{h}^{2}}+{{r}^{2}}\] Here, \[25{{x}^{2}}=16{{x}^{2}}+{{r}^{2}}\] \[r=3x\] Area \[=\sqrt{21(10)(6)(5)}=30\sqrt{7}\,sq\,cm.\] \[\therefore \]height\[=\frac{30\sqrt{7}}{8}=\frac{15\sqrt{7}}{4}cm.\]
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