The diagonal of a square of side a is

1. A diagonal divides the square into two right triangles. 2. Each has legs a and a, hypotenuse d. 3. d^2 = a^2 + a^2 = 2 a^2. 4. So d = a sqrt(2). _Source: Selina Concise Mathematics Class 9, Ch on Pythagoras Theorem (Mistral OCR'd PDF), section on diagonal of square_