SOLUTION: The area of the largest rectangle inscribed in a circle of radius 5 cm is a)25 cm^2 b)50 cm^2 c) 100 cm^2 d)10 square root(2)cm^2 e) 20 square root(2)cm^2

Algebra ->  Surface-area -> SOLUTION: The area of the largest rectangle inscribed in a circle of radius 5 cm is a)25 cm^2 b)50 cm^2 c) 100 cm^2 d)10 square root(2)cm^2 e) 20 square root(2)cm^2       Log On


   



Question 237226: The area of the largest rectangle inscribed in a circle of radius
5 cm is
a)25 cm^2 b)50 cm^2 c) 100 cm^2 d)10 square root(2)cm^2 e) 20 square root(2)cm^2

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
The circle has a diameter of 10 cm. Let x= length of the side of the square. Draw the circle of diameter 10, showing the square with side of x inside the circle. You will see a right triangle, so by Theorem of Pythagoras

x%5E2+%2B+x%5E2+=+10%5E2
2x%5E2=+100
x%5E2+=+50

Now this looks ugly, but remember that all you need to find is the AREA of the square. The area is x%5E2, so this is the answer to the question:

Area = x%5E2=50 sq cm.

Dr. Robert J. Rapalje