Let A 1 = x , y : x ≤ y 2 , x + 2 y ≤ 8 and A 2 = x , y : x + y ≤ k . If 27 (Area A 1 ) = 5 (Area A 2 ), then k is equal to

Step-by-step solution

A 1 = x , y : x ≤ y 2 , x + 2 y ≤ 8 and A 2 = x , y : x + y ≤ k Area A 1 = 2 ∫ 0 2 y 2 d y + ∫ 2 4 8 - 2 y d y = 2 y 3 3 0 2 + 8 y - y 2 2 4 Area A 1 = 2 × 20 3 = 40 3 Area A 2 = 4 × 1 2 k 2 Area A 2 = 2 k 2 Given 27 Area   A 1 = 5 Area   A 2 ⇒ 27 × 40 3 = 5 × 2 k 2 ⇒ k = 6