Home
Class 12
MATHS
A rectangular sheet of fixed perimeter w...

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

A

`24`

B

`32`

C

`45`

D

`60`

Text Solution

Verified by Experts

The correct Answer is:
A, C
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Exersise-3 Part II|22 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise High Level Problems (HLP)|35 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Exersise-2 Part IV comprehension|7 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

Similar Questions

Explore conceptually related problems

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 (a) 24 (b) 32 (c) 45 (d) 60

The area of a rectangular sheet is 500 cm^2. If the length of the sheet is 25 cm, what is its width? Also find the perimeter of the rectangular sheet.

The sum of the areas of two squares is 85. If the sides of both squares have integer lengths, what is the least possible value for the length of a side of the smaller square?

If the rate of change of area of a square plate is equal to that of the rate of change of its perimeter, then length of the side, is

The volume of a cubical box is 32.768 cubic metres. Find the length of a side of the box.

The area of a square and a rectangle are equal.If the side of the square is 40 cm and the breadth of the rectangle is 25 cm,find the length of the rectangle. Also,find the perimeter of the rectangle.

The area of a square and a rectangle are equal. If the side of the square is40 cm and the breadth of the rectangle is 25 cm, find the length of therectangle. Also, find the perimeter of the rectangle.

If the area of a square is numerically equal to its perimeter, then the length of each side is

A box of maximum volume with top open is to be made by cutting out four equal squares from four corners of a square tin sheet of side length a feet and then folding up the flaps. Find the side of the square cut-off.

The area of a square park is the same as of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.

RESONANCE ENGLISH-APPLICATION OF DERIVATIVES-Exersise-3 Part I
  1. If f(x) is a polynomial of degree 4 having extremum at x=1,2 and lim(x...

    Text Solution

    |

  2. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  3. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  4. The number of distinct real roots of x^4-4x^3+12 x 62+x-1=0i sdot

    Text Solution

    |

  5. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  6. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  7. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

    Text Solution

    |

  8. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  9. A vertical line passing through the point (h, 0) intersects the ellips...

    Text Solution

    |

  10. The funciton f(X) =2|x|+|x+2|-||x+2|-|x|| has a local mimimum or a lo...

    Text Solution

    |

  11. Let f:[0,1]rarrR be a function. Suppose the function f is twice differ...

    Text Solution

    |

  12. Let a in R and let f: Rvec be given by f(x)=x^5-5x+a , then (a) f(x...

    Text Solution

    |

  13. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

    Text Solution

    |

  14. A cylindrical container is to be made from certain solid material with...

    Text Solution

    |

  15. Let f,g:[-1,2]vecR be continuous functions which are twice differentia...

    Text Solution

    |

  16. Let f:Rrarr(0,oo)andg:RrarrR be twice differentiable functions such th...

    Text Solution

    |

  17. If f:R->R is a twice differentiable function such that f''(x) > 0 for ...

    Text Solution

    |

  18. If f:R is a differentiable fucntion such that f(x) gt 2f(x) for all x...

    Text Solution

    |

  19. If f(x) = \begin{vmatrix} cos2x & cos2x & sin2x \\ -cosx & cosx & -...

    Text Solution

    |

  20. For every twice differentiable function f: R to [-2,2] with (f^(0))^(2...

    Text Solution

    |