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What is the length x of a side of the small inner square?
It is a common misconception that the length of the side of a small inner square is always x. However, this is not always the case – in fact, the length of the side of a small inner square can actually be quite variable! In this article, we’ll explore what actually determines the length of the side of a small inner square, and how it can vary from case to case.
The Length of a Side of the Small Inner Square
The length of a side of the small inner square is denoted by x. To find the value of x, we must first determine the lengths of the other sides of the square. The length of the side of the large outer square is denoted by L. The difference between the lengths of the two squares is denoted by d.
We can set up a proportion to solve for x:
L/x = (L-d)/(L-2x)
Cross-multiplying, we get:
Lx = (L-d)(L-2x)
Expanding, we get:
Lx = LL -dL -2Lx +2dx
Collecting terms, we get:
3Lx = LL -dL +2dx
Dividing both sides by 3, we get:
x = (LL -dL +2dx)/3L
It is impossible to determine the length x of a side of the small inner square without more information. However, we can use the given information to make some conjectures. Based on the given information, it seems that the length of x is likely to be less than 3 and greater than 1.5.
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