Question

A square has a side length of 4 centimeters. What is the length of the diagonal of the square? What is the length from the corner to the center of the square?​

Answer 1

4
`√(2)` cm AND 2
`√(2)` cm

Explanation:

The length of a diagonal of a square means finding the hypotenuse (long side) of a right triangle with legs of the length of the side of the square. This means you can use a^2 + b^2 = c^2 to solve for the diagonal. Plugging in your values gets you 4^2 + 4^2 = c^2, simplify to get 16 + 16 = c^2, simplify further to get 32 = c^2. Isolate c by taking the square root of both sides to get
`√(32)` = c, which you can simplify by listing out the factors of 32 and finding pairs. 32 = 2 * 2 * 2 * 2 *2 (5 of them), meaning its square root is 4
`√(2)`, which is the length of the diagonal. Don't forget your units! (:

For the second part, remember that the distance between the corner to the center of a square is half the diagonal of the square. You already have the length of that diagonal, so all you have to do is divide it by 2. Do so and you get 2
`√(2)`. Once again, don't forget your units! (:

If you're required to give decimal estimates, then pop those final answers into a calculator and round to the specified number of decimal places. No one will ask you to calculate irrational square roots, or at least no one should.