Home
Class 12
MATHS
A triangular park is enclosed on two sid...

A triangular park is enclosed on two sides of a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is

A

`sqrt((x^(3))/(8))`

B

`(1)/(2) x^(2)`

C

`pi x^(2)`

D

`(3)/(2) x^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE - 2 (LEVEL - II)|15 Videos
  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE - 3|32 Videos
  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE -1 (SECTION- F )|2 Videos
  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-II)|28 Videos
  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos

Similar Questions

Explore conceptually related problems

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. Two having fence are of same length x. The maximum area enclosed by the park is :- (a) 1/2 x^2 (b) pix^2 (c) 3/2 x^2 (d) sqrt(x^3/8)

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank.Two having fence are of same length x. The maximum area enclosed by the park is:-

A triangle has a perimeter of 200. If two of its sides are equal and the third side is 20 more than the equal sides, what is the length of the third side?

Which of the following can be the length of the third side of a triangle whose two sides measure 18 cm and 14 cm?

If length of two sides of a triangle are 6 cm and 10 cm, then the length of the third side can be

The length of two sides of a triangle are 7 cm and 9 cm. The length of the third side may lie between

A given rectangular area is to be fenced off in a field whose length lies aong a straight river. If no fencing is needed along the river,show that the least length of fencing will be required when length of the field is twice its breadth.

A cow is tied to a corner (vertex) of a regular hexagonal fenced area of side a metres by a rope of length 5a/2 metres in a grass field. (The cow cannot graze inside the fenced area.) What is the maximum possible area of the grass field to which the cow has access to graze ?

In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. If x^2-c^2=y , where c is the length of the third side of the triangle, then the circumradius of the triangle is c/sqrtk . The value of k is _________.

MOTION-MAXIMA AND MINIMA -EXERCISE -2 (LEVEL- I)
  1. The lower corner of a leaf in a book is folded over so as to reach the...

    Text Solution

    |

  2. The latest edge of a regular hexagonal pyramid is 1c mdot If the volum...

    Text Solution

    |

  3. A triangular park is enclosed on two sides of a fence and on the third...

    Text Solution

    |

  4. Find the maximum slope of the curve y=-x^3+3x^2+2x-27 .

    Text Solution

    |

  5. If x1 and x2 are abscissae of two points on the curve f(x) = x - x^2 i...

    Text Solution

    |

  6. The maximum value of f(x) = 2bx^2 - x^4 -3b is g(b), where b gt 0. If ...

    Text Solution

    |

  7. The function 'f' is defined by f(x)=x^p(1-x)^q for all x\ in R , whe...

    Text Solution

    |

  8. If f(x)=(x^2-1)/(x^2+1) . For every real number x , then the minimum v...

    Text Solution

    |

  9. If f(x)=alog|x|+b x^2+x has its extremum values at x=-1a n dx=2, then ...

    Text Solution

    |

  10. Which of the following point lying on the line x + 2y = 5 is at minimu...

    Text Solution

    |

  11. The maximum distance of the point (a, 0) from the curve 2x^(2) + y^(2)...

    Text Solution

    |

  12. The point on the line y = x such that the sum of the squares of its di...

    Text Solution

    |

  13. if the complete set of values (s) of 'a' for which the function f (x)...

    Text Solution

    |

  14. If the point (1,3) serves as the point of inflection of the curve y =...

    Text Solution

    |

  15. The equation x^(3) - 3x + [a] = 0 , will have three real and distinct ...

    Text Solution

    |

  16. Solution(s) of the equation. 3x^2-2x^3 = log2 (x^2 + 1) - log2 x is/ar...

    Text Solution

    |

  17. Let f(x)=x^(3) +3(a-7)x^(2)+3(a^(2) -9) x-1. If f(x) has positive po...

    Text Solution

    |

  18. If the function f(x) = x^3-9x^2 +24x + c has three real and distinct r...

    Text Solution

    |

  19. A and B are the points (2, 0) and (0, 2) respectively. The coordinates...

    Text Solution

    |

  20. Two points A(1, 4) & B(3, 0) are given on the ellipse 2x^(2) + y^(2) =...

    Text Solution

    |