CAMBRIDGE UNIVERSITY ADMISSION TEST – GEOMETRY

This geometry question was set on a Cambridge University admissions test in 2023. Every corner of the rectangle touches a side of the square, the area is 20, and the exam asks for the largest possible length of one piece. Why "largest"? Because the diagram is not to scale, and the same rectangle fits two ways. CHAPTERS 0:00 The Cambridge question 0:27 Naming every piece 1:11 Square minus four triangles 1:53 The two small triangles make a square 2:27 The two big triangles make a square 2:55 Solving the equation 4:01 The quadratic formula 5:05 Why there are two answers