Double Hearts Ratio Puzzle - Solution
The Puzzle:
Which is bigger: the total area of orange or the total area of red?
Author: Peter Grabarchuk
This Puzzle © 2008 Peter Grabarchuk. All Rights Reserved.
More from Peter Grabarchuk at PeterPuzzle.com
Author: Peter Grabarchuk
This Puzzle © 2008 Peter Grabarchuk. All Rights Reserved.
More from Peter Grabarchuk at PeterPuzzle.com
Our Solution:
Using the illustration below, we can calculate the following areas:
The red area is two circles, one of radius 3, the other of radius 2.
Area of big red circle = π×32 = 28.27 (to 2 decimals)
Area of small red circle = π×22 = 12.57 (to 2 decimals)
So we have:
A(square) = 9 x 9 = 81;
A(red) = 28.27 + 12.57 = 40.84;
A(orange) = 81 - 40.84 = 40.16.
Thus, A(red) > A(orange).
Author: Peter Grabarchuk
This Puzzle © 2008 Peter Grabarchuk. All Rights Reserved.
The red area is two circles, one of radius 3, the other of radius 2.
Area of big red circle = π×32 = 28.27 (to 2 decimals)
Area of small red circle = π×22 = 12.57 (to 2 decimals)
So we have:
A(square) = 9 x 9 = 81;
A(red) = 28.27 + 12.57 = 40.84;
A(orange) = 81 - 40.84 = 40.16.
Thus, A(red) > A(orange).
Author: Peter Grabarchuk
This Puzzle © 2008 Peter Grabarchuk. All Rights Reserved.
Puzzle Author: Grabarchuk, Peter
See this puzzle without solution
Discuss this puzzle at the Math is Fun Forum