Question

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....

Answer 1

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 ....... ????

Answer 2

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