Factoring an area?
Four rectangles with all integer side lengths are tiled together to form a square, as shown.
The numbers inside two rectangles represent their respective areas.
What is the sum of the areas of the other two rectangles?
The answer is 158.
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1 solution
Since they all have integer side lengths, the first rectangle can be 11×3 or 33×1, while the second can be 13×5 or 65×1. But, since they form a square, the sum of a side length of the first rectangle and the second rectangle has to be the same as the sum of the remaining two.
That is, if the rectangles are a×b and c×d then a+c=b+d = side length of the square.
In this problem, the only suitable case for the rectangles are 11×3 and 13×5, since 11+5=13+3=16. Thus, the area of the square is 16×16 = 256
Hence, area of the remaining portion = Area of square - (65+33) =256 - 98 =158