Posted by **Ashley** on Tuesday, January 29, 2013 at 8:45am.

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 -
**Ashley**, Tuesday, January 29, 2013 at 8:52am
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 -
**Norman**, Tuesday, January 29, 2013 at 10:04am
Ok

- Math -
**Ashley**, Tuesday, January 29, 2013 at 10:44am
ok....

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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