Home
Class 12
MATHS
A rectangle is inscribed in an equilater...

A rectangle is inscribed in an equilateral triangle of side length `2a` units. The maximum area of this rectangle can be `sqrt(3)a^2` (b) `(sqrt(3)a^2)/4` `a^2` (d) `(sqrt(3)a^2)/2`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BANSAL|Exercise All Questions|425 Videos

Similar Questions

Explore conceptually related problems

If a rectangle is inscribed in a equilateral triangle of side 2sqrt2 then side of maximum area of rectangle is

The area of an equilateral triangle with side 2sqrt3 cm is

If a rectangle is inscribed in an equilateral triangle of side length 2sqrt(2) as shown in the figure, then the square of the largest area of such a rectangle is_______.

In an equilateral triangle with side a, prove that area =(sqrt(3))/(4)a^(2)

The area of an equilateral triangle is 4sqrt(3)cm^(2). . Find the length of each side of the triangle

If area of a circle inscribed in an equilateral triangle is 48pi square units, then perimeter of the triangle is (a) 17sqrt(3) units (b) 36 units (c) 72 units (d) 48sqrt(3) units

BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. If the sum of the lengths of the hypotenuse and another side of a righ...

    Text Solution

    |

  2. Find the point (alpha,beta) on the ellipse 4x^2+3y^2=12 , in the first...

    Text Solution

    |

  3. A rectangle is inscribed in an equilateral triangle of side length 2a ...

    Text Solution

    |

  4. Tangents are drawn to x^2+y^2=16 from the point P(0, h)dot These tange...

    Text Solution

    |

  5. f(x)=x^(1/5) at x=0 has inflection point. y"\ DdotNdotEdot\ at x=0

    Text Solution

    |

  6. f(x)=x^3a t\ x=0 has inflection point y ' '=0 at x=0 and change sign.

    Text Solution

    |

  7. f(x)=|x^2-1| has no inflection point in its domain as no tangent ca...

    Text Solution

    |

  8. Number of points of inflection for f(x)=x^2e^(-|x|) is 1 (b) 2 (...

    Text Solution

    |

  9. Find the value of a if x^3-3x+a=0 has three distinct real roots.

    Text Solution

    |

  10. Prove that there exist exactly two non-similar isosceles triangles A B...

    Text Solution

    |

  11. Find the set of value of m for the cubic x^3-3/2x^2+5/2=(log)(1/4)(...

    Text Solution

    |

  12. The set of value(s) of a for which the function f(x)=(a x^3)/3+(a+2)x^...

    Text Solution

    |

  13. The number of values of k for which the equation x^3-3x+k=0 has two di...

    Text Solution

    |

  14. Find the shortest distance between the curves y^2=x^3a n d\ 9x^2+9y...

    Text Solution

    |

  15. let f(x)=-x^3+(b^3-b^2+b-1)/(b^2+3b+2) if x is 0 to 1 and f(x)=2x-3 if...

    Text Solution

    |

  16. If the function f(x)=(a+3)x^3+(a-3)x^2+4(a-4)x+5 has maxima at some x...

    Text Solution

    |

  17. Find a point M on the curve y=3/(sqrt(2))\ \ xlnx ,\ x\ in (e^(-1. 5)...

    Text Solution

    |

  18. Assuming the petrol burnt (per hour) in driving a motor boat veries as...

    Text Solution

    |

  19. Find the point on the curve y=x/(1+x^2), where the tangent to the curv...

    Text Solution

    |

  20. Discuss the extremum of f(x)=asecx+bcos e cx ,0ltaltb

    Text Solution

    |