SOLUTION: Determine the dimensions of a rectangle of area 60 in^2 that is inscribed in a circle of radius 6.5 inch.

Algebra ->  Test -> SOLUTION: Determine the dimensions of a rectangle of area 60 in^2 that is inscribed in a circle of radius 6.5 inch.       Log On


   

Question 850276: Determine the dimensions of a rectangle of area 60 in^2 that is inscribed in a circle of radius 6.5 inch.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
The diameter of the circle is the same length as the diagonal of the rectangle. 6.5%2A2=13 inches, the diameter.

x and y, the dimensions of the rectangle.
x%5E2%2By%5E2=13%5E2, because the diagonal, diameter, is also the hypotenuse of each of the two right triangles composing the rectangle.

xy=60, area of the rectangle.

SYSTEM TO SOLVE:
----------------
x^2+y^2=169
-----------
xy=60
----------------

y=60/x.
x%5E2%2B%2860%2Fx%29%5E2=169
x%5E4%2B60=169x%5E2
x%5E4-169x%5E2%2B60=0
-
First solve for x%5E2; you'll want the choice with the positive square root using general solution...
Discrim, 169^2-4*60=28561-240=28321=127*223, prime factored.
x%5E2=%28169%2Bsqrt%2828321%29%29%2F2
-
highlight%28x=sqrt%28%28169%2Bsqrt%2828321%29%29%2F2%29%29
-
y=60%2Fx=60%2F%28sqrt%28%28169%2Bsqrt%2828321%29%29%2F2%29%29
highlight%28y=60%2Asqrt%282%29%2Fsqrt%28169%2Bsqrt%2828321%29%29%29


-
You could continue and rationalize the denominator more thoroughly