A rectangular sheet of fixed perimeter with sides having their lengths in the ratio `8: 15` is converted into anopen 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 length of the sides of the rectangular sheet are 24 (b) 32 (c) 45 (d) 60

Explanation

Let the sides of rectangle be 15k and 8k and side of square be x then (15k -2x) (8k-2x) x is volume
`v=2(2x^(3))-23kx^(2)+60k^(2)x)`
`(dv)/(dx)|_(x=5)=0` or `6x^(2)-46kx+60k^(2)|_(x=5)=0`
or `6k^(2)-23k+15-=0`
or `k=3, k=5/6`
only k=3 is permissiable
So the sides are 45 nd 24