Home
Class 12
MATHS
Show that all rectangles with a given pe...

Show that all rectangles with a given perimeter, the square has the maximum area.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    BODY BOOKS PUBLICATION|Exercise EXERCISE|53 Videos

Similar Questions

Explore conceptually related problems

Prove that of all rectangles with given area square has minimum perimeter?

The length of a rectangle is 10 centimetes more, than its breadth and its area is 144 square centimetres. What are the length and breadth?

Among an equilateral triangle, a square, a regular hexagon and a circle, all with the same perimeter, which has the largest area?

The perimeter of a square is 14 metres. What is its area?

Draw a rectangle of perimeter 15 cm and sides are in the 3:4 .

Draw a rectangle of perimeter 18 cm and sides are in the ratio 3:2.

In writing the equation to construct a rectangle of specified perimeter and area, the perimeter,was wrongly written as 24 instead of 42.The length of a side was then computed as 10 metres.What is the area in the problem?What are the lengths of the sides of the rectangle in the correct problem?

'Draw a rectangle of length 4 centimetres and breadth 2 centimetres. Draw a square having, the same area of the rectangle.

Of four equal equilateral triangles, two are cut vertically into halves and two whole are put together to make a rectangle: If a side of the triangle ls 1 metre, what is the area and the perimeter of the rectangle?

BODY BOOKS PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. Which of the following function is always increasing? a)x+sin2x b)x-s...

    Text Solution

    |

  2. The radius of a cylinder increases at a rate of 1 cm/s and its height ...

    Text Solution

    |

  3. Write the equation of tangent at (1,1) on the curve 2x^2+3y^2=5.

    Text Solution

    |

  4. Which of the following function is increasing for all values of x in i...

    Text Solution

    |

  5. Find a point on the curve y=(x-2)^2 at which the tangent is parallel t...

    Text Solution

    |

  6. Find the maximum profit that a company can make, if the profit functio...

    Text Solution

    |

  7. Find the slope of the normal to the curve y=sintheta at theta=pi/4

    Text Solution

    |

  8. Show that the function x^3-6x^2+15x+4 is strictly increasing in R.

    Text Solution

    |

  9. Show that all rectangles with a given perimeter, the square has the ma...

    Text Solution

    |

  10. Show that the function x^3-3x^2+6x-5 is strictly increasing on R.

    Text Solution

    |

  11. Find the interval in which the function f(x)=sinx+cosx, 0lexle2pi is s...

    Text Solution

    |

  12. The slope of the tangent to the curve y=x^3-1 at x=2 is………

    Text Solution

    |

  13. Use differentiation to approximate sqrt36.6.

    Text Solution

    |

  14. Find two numbers whose sum is 24 and whose product as large as possibl...

    Text Solution

    |

  15. Find the equation of the tangentto the ellipse x^2/a^2+y^2/b^2=1at(x1,...

    Text Solution

    |

  16. Find the intervals in which the function f(x)= 2x^3-15x^2+36x+1 is i...

    Text Solution

    |

  17. Find the intervals in which the function f(x)=2x^3-15x^2+36x+1 is inc...

    Text Solution

    |

  18. Find the approximate value of (626)^(1//4).

    Text Solution

    |

  19. Find two positive numbers x and y such that x+y=60 and x y^3 is maximu...

    Text Solution

    |

  20. If the radius of a sphere is measured as 9 m with an error of 0.03 m, ...

    Text Solution

    |