On the EdgePro Problems > Math > Geometry > Rectangles and Squares
On the Edge
Square X has sides of length n units. Its interior is filled with squares of side length 1 unit.
These same unit squares could be taken from the interior of X and placed along the edges of square Y, so that all the unit squares are on the exterior of square Y, with a single edge of each unit square against an edge of Y, and no part of any edge of Y does not touch a unit square.
There are two more squares, which are non-overlapping: H and K. The length of a side of K is 4 less than the length of a side of H. All the unit squares could be placed on the interior of squares H and K, with at least one edge of each unit square against an edge of either H or K, and such that no part of any edge of H or K does not touch a unit square.
If the sides of square H are 5 units shorter than the sides of square Y, how many unit squares are there?
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