Two diagonals p , q of a quadrilateral satisfy ∣ p − q ∣ = p ⋅ q , ∣ p ∣ = 1 , ∣ q ∣ = 2 . The area of the quadrilateral is

Question

Two diagonals p ​ , q ​ of a quadrilateral satisfy ∣ p ​ − q ​ ∣ = p ​ ⋅ q ​ , ∣ p ​ ∣ = 1 , ∣ q ​ ∣ = 2 ​ . The area of the quadrilateral is

TestHub · Accepted Answer

Squaring gives 3 − 2 2 ​ cos θ = 2 cos 2 θ , whose admissible value gives sin θ = 1/ 2 ​ . Thus area = 2 1 ​ ∣ p ​ × q ​ ∣ = 2 1 ​ .

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