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Find the dimensions of the rectangle of ...

Find the dimensions of the rectangle of maximum perimeter that can be inscribed in a circle of radius a.

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The correct Answer is:
Length = breadth `=sqrt(2a)`
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CHHAYA PUBLICATION-MAXIMA AND MINIMA -EXERCISE Short Answer Type Questions
  1. Find the critical points of each of the following functions : f(x)=...

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  2. The perimeter of a rectangle is 100 cm. If the area of the rectangle ...

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  3. Show that , of all rectangles of given permeter , the square has the g...

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  4. Prove that , of all rectangles of given area , the square has the leas...

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  5. Find the dimensions of the rectangle of maximum perimeter that can be ...

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  6. The perimeter of a triangle is 8 cm .If one of the sides is 3 cm , fin...

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  7. A printed page is to contain 96cm^(2) of printed area , a margin of 1....

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  8. The height of a particle projected with velocity u at an angle alpha ...

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  9. What will be the radius of the base of a solid circular cylinder of vo...

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  10. The function f(x)=4x^(3)+ax^(2)+bx+2 has an extremum at (2,-2) , find...

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  11. The cost c of manufacturing a certain article is given by the formula...

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  12. Determine when will the function sin3x-3sinx will be greatest or least...

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  13. Obtain the maximum and minimum values of the function cos^(2)x+cosx+3 ...

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  14. Find the maximum and minimum values of : 3cosx+4sinx

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  15. Find the maximum and minimum values of : cos^(2)x-cosx(0lexle(pi)...

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  16. Find the maximum and minimum values of : sinx+cos^(2)x((pi)/(2)lt...

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  17. Find the maximum and minimum values of : 1+2sinx+3cos^(2)x(0lexl...

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  18. Prove that function y=(x-a(1))^(2)+(x-a(2))^(2)+...+(x-a(n))^(2) is...

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  19. If Agt0,Bgtgt0andA+B=(pi)/(3), find the maximum value of tan A tan B .

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  20. Prove that f(x)=cosx-1+(x^(2))/(2!)-(x^(4))/(4!) possesses a maximum ...

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