SOLUTION: A rectangle is inscribed in a circle of radius √10.If the area of the rectangle is 16,find its dimensions.

Since the radius of the circle is  ,  its diameter is  .


The diagonal of the rectangle is the diameter of the circle.


So, if x and y are the rectangle dimension, we have these two equations


    x^2 + y^2 =  = 40,     (1)

    xy = 16.                        (2)


It implies


    x^2 + 2xy + y^2 = 40 + 2*16 = 72

    x^2 - 2xy + y^2 = 40 - 2*16 =  8,

or

     = 72,

     =  8.


Taking square roots from both sides of the equations, we get


    x + y =     (3)

    x - y = .   (4)


By adding      equations  (3) and (4), you get  2x = ;  hence,  x = .

By subtracting equations  (3) and (4), you get  2y = ;  hence,  y = .


ANSWER.  The dimensions of the rectangle are    and  .