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OPQR is a square and M, N are the mid points of the sides PQ and QR respectively. If the ratio of the areas of the square and the triangle OMN is λ : 6, then λ 4 is equal to ________

Correct answer

4

Step-by-step solution

We can assume that OP and OR are x–axis and y–axis respectively. Let OP = a, then area (square OPQR) = a 2 Coordinate of M and N are a , a 2 and a 2 , a respectively. ∴ area (∆OMN) = 1 2 a a / 2 a / 2 a = 3 a 2 8 ∴ 8 3 = λ 6 ∴ λ = 16 ⇒ λ 4 = 16 4 = 4

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