question_answer

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

\[=2\times 75\sqrt{15}\,c{{m}^{2}}=150\sqrt{15}\,c{{m}^{2}}\]