posted by Ashley on .
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....
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 ....... ????
so is next step take the first derv of the area
Area of rect '= -1/2(4-b^2) + (4-2^2)^1/2