A rectangle is made up from six squares. Find side length of the largest square if side length of the smallest square is 1.
This shape below is made up from squares.
Find side length of the bottom square if side length of the smallest square is equal to 1.
You are given a convex quadrilateral. Is it always possible to cut out a parallelogram out of the quadrilateral such that three vertices of the new parallelogram are the vertices of the old quadrilateral?
The area of a rectangle is 1 cm\(^2\). Can its perimeter be greater than 1 km?
Ben is going to bend a square sheet of paper \(ABCD\). Ben calls the fold beautiful, if the side \(AB\) crosses the side \(CD\) and the four resulting rectangular triangles are equal. Before that, Jack selects a random point on the sheet \(F\). Find the probability that Ben will be able to make a beautiful fold through the point \(F\).
A square is cut by 18 straight lines, 9 of which are parallel to one side of the square and the other 9 parallel to the other – perpendicular to the first 9 – dividing the square into 100 rectangles. It turns out that exactly 9 of these rectangles are squares. Prove that among these 9 squares there will be two that are identical.