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Questions  

OPQR is a square and M, N are the middle points of the sides PQ and QR, respectively. Then the ration of the area of the square to that of triangle OMN is 

a
4:1
b
2:1
c
8:3
d
7:3

detailed solution

Correct option is C

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

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