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Prove that the area of right-angled tria...

Prove that the area of right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.

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MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. A wire of length 36 cm is cut into two pieces . One of the pieces is t...

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  2. Prove that the perimeter of a right-angled triangle of given hypotenus...

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  3. Prove that the area of right-angled triangle of given hypotenuse is ma...

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  4. Prove that the least perimeter of an isosceles triangle in which a cir...

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  5. Show that, of all the rectangles with a given area, the square has the...

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  6. Show that rectangle of maximum perimeter, which can be inscribed in a ...

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  7. Show that of all rectangles inscribed in a given circle the square has...

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  8. A rectangle is inscribed in a semi-circle of radius 'r' with one of it...

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  9. Of all rectangles , each of which has perimeter: 40 cm . Find the one ...

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  10. Of all rectangles , each of which has perimeter: 60 cm . Find the one ...

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  11. An open box with a square base is to be made out of a given iron sheet...

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  12. Show that the semi-vertical angle of the cone of the maximum volume an...

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  13. Show that the semi-vertical angle of the right-circular cone of maximu...

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  14. Prove that the semi-vertical angle of the right circular cone of given...

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  15. Show that height of the cylinder of greatest volume which can be inscr...

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  16. Show that the volume of the greatest cylinder, which can be inscribed ...

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  17. Show that the altitude of the right circular cone of maximum volume th...

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  18. Prove that volume of largest cone, which can be inscribed in a sphere,...

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  19. Show that the right circular cone of least curved surface and given vo...

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  20. Show that the height of the cylinder of maximum volume that can be ins...

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