What is the length of the diagonal of a square with side length 3?

• A. 3
• B. 3√3
• C. 3√2
• D. 6

Answer: (C)

The diagonal of a square forms the hypotenuse of a right triangle whose legs are the two sides of the square. Since each side is 3, the diagonal satisfies diagonal^2 = 3^2 + 3^2 = 9 + 9 = 18. So diagonal = sqrt(18) = sqrt(9·2) = 3√2. This is a standard result: the diagonal of a square with side length s is s√2, so for s = 3 the length is 3√2.