A) 18cm
B) 12cm
C) 15cm
D) 25cm
Correct Answer: C
Solution :
In \[\Delta \Alpha \Beta CD\]let a = 12cm, b = 17 cm and c = 25 cm. \[\therefore \]Semi-perimeter of \[\Delta \Alpha \Beta CD.\] \[S=\left( \frac{12+17+25}{2} \right)cm\,=\frac{54}{2}\,cm=27\,cm\] \[\therefore \] Area of \[\Delta BCD\] \[=\sqrt{27(27-12)(27-17)(27-25)}\,c{{m}^{2}}\] \[=\sqrt{27\times 15\times 10\times 2}\,c{{m}^{2}}=90\,c{{m}^{2}}\] Now, area of parallelogram ABCD \[=2\times \]Area of\[\Delta BCD\] \[=(2\times 90)c{{m}^{2}}=180\,c{{m}^{2}}\] ?(i) Let altitude of parallelogram ABCD from vertex A be h cm. Also, area of parallelogram\[\text{=}\,\text{Base}\,\text{ }\!\!\times\!\!\text{ }\,\text{Altitude}\] \[\Rightarrow \]\[180=DC\times h\] [From (i)] \[\Rightarrow \]\[180=12\times h\] \[\therefore \] \[h=\frac{180}{12}=15\] Required length of the altitude is 15 cm.
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