A) 4 : 1
B) 2 : 1
C) 8 : 3
D) 7 : 3
Correct Answer: C
Solution :
Let the coordinates of vertices O, P, Q, R be (0, 0), (a, 0), (a, a), (0, a), respectively. Then, we get the coordinates of M as (a, a/ 2) and those of N as (a / 2, a) Therefore, area of \[\Delta OMN\] is \[\frac{1}{2}\left| \begin{matrix} 0 & 0 & 1 \\ a & a/2 & 1 \\ a/2 & a & 1 \\ \end{matrix} \right|=\frac{3{{a}^{2}}}{8}\] Area of the square is \[{{a}^{2}}.\]Hence, the required ratio is 8 : 3.You need to login to perform this action.
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