Final answer:
To find the size of the square that must be cut from each corner, assign the variable 'x' to represent this dimension. Formulate an equation based on the given base area, and solve this quadratic equation. The solution will provide the length of the side of the square, which should be then rounded to the nearest tenth.
Step-by-step explanation:
The subject of this problem is mathematics, specifically the concept of geometry and volume. Let's start by defining 'x' as the length of a side of the square to be cut from each corner. Once the squares are cut, the dimensions of the box become (25-2x) and (16-2x) in terms of length and width.
As given, the base area of the box should be 252 in², which means that the product of length and width of the resulting box should be 252. Writing it as an equation, we have (25-2x)*(16-2x)=252. Solving this equation for 'x' will yield the length of the side of the square that needs to be cut from each corner, which can subsequently be rounded to the nearest tenth.
Please note that this equation happens to be a quadratic equation and can be solved by using the quadratic formula or factoring, if possible. However, without the actual numerical solution, I would recommend solving this equation using a graphing calculator or an online math tool to accurately find the value for 'x'.
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