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A mechanical engineering student wishes to inscribe a rectangle in a quarter circle of radius 2.00 cm. Determine the dimensions of the rectangle that will give it the greatest area.

length in cm =
height in cm =

My attempt on find the relationship between the rectangle and the quarter circle:

Let the base of the rectangle = b
let the height of the rectangle = h
Area of a a rectangle = b*h

Area of a circle =pie*R^2
Quarter of a circle = 1/4 pie R^2

am I on the right track......
is this the correct thought process....

  • Math -

    Would it be safe to say that the the diagonal line in the rectangle could equal r = 2.

    so I could use
    b^2+ h^2 =r^2
    solve for h
    h= Square root ( r^2 -b^2)
    Area = b^2 * Square root (r^2-b^2)
    area = b*(r^2-b^2)^1/2 ....... ????

  • Math -


  • Math -

    so is next step take the first derv of the area

    Area of rect '= -1/2(4-b^2) + (4-2^2)^1/2

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