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What is the length x of a side of the small inner square? Drawing is enclosed in OS link

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Answer: (b-a)^2, {(b-a)^2}/4

Step-by-step explanation:

One side of the big square = b-a, therefore,

(total area of big square =(b-a)^2

The four inner triangles are equal because they are divided by diagonal lines of a square. So area of one triangle will be: area of square/4. So,

Area of each of 4 inner triangles= ( {b-a)^2} /4

From the image attached, I've drawn the diagram to reflect what the question is saying. The sides of the small inner square are connected by mid points of inner triangle sides.

By symmetry, we can tell that the area of this small square would be a quarter of that of the big square seeing that the sides of this small square will be half of the side of the big square.

Therefore, area of small square =

{(b-a)^2}/4

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