OPQR is a square and M, I{ are the middle points of the sides PQ and QR, respectively, Then the ratio of the area of the square to that of triangle OMN is

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 ΔOMN=12001aa/21a/2a1=3a28The area of the square is a2.Hence, the required ratio is 8 : 3.