Let the points ( 2 11 , α ) lie on or inside the triangle with sides x + y = 11 , x + 2 y = 16 and 2 x + 3 y = 29 . Then the product of the smallest and the largest values of α is equal to :

Question

Let the points ( 2 11 ​ , α ) lie on or inside the triangle with sides x + y = 11 , x + 2 y = 16 and 2 x + 3 y = 29 . Then the product of the smallest and the largest values of α is equal to :

TestHub · Accepted Answer

Clearly, x = 2 11 ​ intersect x + y − 11 = 0 at ( 2 11 ​ , 2 11 ​ ) and 2 x + 3 y − 29 = 0 at ( 2 11 ​ , 6 ) ⇒ α = [ 2 11 ​ , 6 ] α m i n ​ ⋅ α m a x ​ = 2 11 ​ ⋅ 6 = 33

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