2015 AMC 8 Problems/Problem 25
One-inch squares are cut from the corners of this 5 inch square. What is the area in square inches of the largest square that can be fitted into the remaining space?
SOLUTION 1 Lets draw a diagram. (Credits to djmathman ) Let us focus on the big triangles taking up the rest of the space. The triangles on top of the unit square between the inscribed square, are similiar to the 4 big triangles by AA. Let the height of a big triangle be then . Which means This means the area of each triangle is This the area of the square is