Talia is building a 12 inch square wooden box and wants to put in a diagonal piece of wood. How long would the piece of wood need to be to the nearest inch?
To find the length of the diagonal piece of wood, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the diagonal is the hypotenuse, and the sides of the square are the other two sides of the right triangle. Since all sides of a square are equal, each side of the square is 12 inches.
Let's call the length of the diagonal "d". Applying the Pythagorean theorem,
d^2 = 12^2 + 12^2
d^2 = 144 + 144
d^2 = 288
d ≈ √288 ≈ 16.97
Therefore, the length of the diagonal piece of wood, to the nearest inch, would be 17 inches.