The area of the parallelogram whose length is 30 cm, width is 20 cm and one diagonal is 40 cm, is |
A) \[100\sqrt{15}\,c{{m}^{2}}\]
B) \[150\sqrt{15}\,c{{m}^{2}}\]
C) \[200\sqrt{15}\,c{{m}^{2}}\]
D) \[300\sqrt{15}\,c{{m}^{2}}\]
Correct Answer: B
Solution :
Both of the triangles made by the diagonals of the parallelogram will be equal in area. |
Now, area of \[\Delta ABC=\sqrt{s\,(s-a)(s-b)(s-c)}\] |
\[=\sqrt{45\,(5)\,(15)\,(25)}=75\sqrt{15}\,c{{m}^{2}}\] |
Thus, area of the parallelogram ABCD |
\[=2\times 75\sqrt{15}\,c{{m}^{2}}=150\sqrt{15}\,c{{m}^{2}}\] |
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