A) 3 cm
B) 6 cm
C) 4 cm
D) 2 cm
Correct Answer: A
Solution :
In \[\Delta ABC,\]a =7 cm, b = 6.5 cm and c = 7.5 cm \[\therefore \] \[s=\left( \frac{7.5+7+6.5}{2} \right)cm=\frac{21}{2}cm=10.5\,cm\] \[\therefore \]Area of\[\Delta \Alpha \Beta C\] \[=\sqrt{10.5(10.5-7.5)(10.5-7)(10.5-6.5)}\,c{{m}^{2}}\] \[=\sqrt{10.5\times 3\times 3.5\times 4}\,c{{m}^{2}}=\sqrt{441}\,c{{m}^{2}}\] \[=21\,c{{m}^{2}}\] Since, Area of \[\Delta \Alpha \Beta C\] = Area of parallelogram BCED \[\therefore \]\[21=BC\times DF\] \[\Rightarrow \]\[21=7\times DF\] \[\Rightarrow \]\[DF=\frac{21}{7}=3\,cm\]
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