A square is divided in two quadrilaterals of given area. What fraction of the square’s perimeter is red?
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Solution
A fraction of 9/16 of the square’s perimeter is red.
First, draw a horizontal line through the middle of the slanted line segment as shown. It is easily seen that the the two formed triangles are congruent. Interchanging their colour therefore has no effect on the red area fraction, neither does it change the perimeter fraction.
Let’s therefore consider the special case with the horizontal divider. The top side of the red rectangle is 1/4 of the total perimeter. The vertical sides are both 5/8*1/4. Adding up gives 9/16.
Please find here a nice solution including an animation of the allowed configuration by Amaresh G S..