JEE Advanced | 2013Application of DerivativeHard
Question
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio of 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners.If the total area of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are
Options
A.24
B.32
C.45
D.60
Solution
Where P = 8 λ + 15 λ + 8 λ +15 λ & λ is constant
Let removed length from each sides is x
Removed area is 4x2 = 100 ⇒ x = 5
V = (8λ - 2x) (15 λ - 2x)x
V = 120l2x - 46λ x2 + 4x3
12λ2 - 92λx + 12x2 = 0
Put x = 5 ⇒ 120λ2 - 4601 + 300 = 0
12λ2 - 40 λ + 30 = 0
6λ2 - 23λ + 15 = 0
( l - 3) (6λ - 5) = 0
= - 29λ + 24x = 120 - 92λ
at = 3
at
(rejected)
Let removed length from each sides is x
Removed area is 4x2 = 100 ⇒ x = 5
V = (8λ - 2x) (15 λ - 2x)x
V = 120l2x - 46λ x2 + 4x3
12λ2 - 92λx + 12x2 = 0Put x = 5 ⇒ 120λ2 - 4601 + 300 = 0
12λ2 - 40 λ + 30 = 0
6λ2 - 23λ + 15 = 0
( l - 3) (6λ - 5) = 0
= - 29λ + 24x = 120 - 92λ at = 3
at
(rejected)Create a free account to view solution
View Solution FreeMore Application of Derivative Questions
The length of subnormal to the curve y2 = 12 ax at any point is-...If a, b, c are positive numbers in G.P. and log , log and log are in A.P., then a, b, c forms the sides of a triangle wh...If a variable tangent to the curve x2y = c3 makes intercepts a, b on x and y axis respectively, then the value of a2b is...Point of inflexion to the curve y = x5/2 is-...The equation of the tangent to the curve 6y = 7 - x3 at point (1, 1) is -...