Question

OPQR is a square and M, N are the middle points of the sides PQ and QR respectively, then the ratio of the areas of the square and the triangle OMN is

• A. 4:1
• B. 8:3
• C. 2:1
• D. 4:3

Answer 1

The correct option is B

8:3

$M=(a,\frac{a}{2}),N=(\frac{a}{2},a)\text{Area}\Delta OMN=\frac{1}{2}\left|\begin{array}{ccc}0& 0& 1\\ a& a/2& 1\\ a/2& a& 1\end{array}\right|=\frac{3a^2}{8},\text{Area of square}=a^2\therefore \text{Ratio is}{a}^2:\frac{3a^2}{8}\Rightarrow 8:3$