talia is building a 12 inch square, wooden box and wants to put in a diagonal piece of wood. how long would the piece need to be to the nereast inch
To find the length of the diagonal piece of wood, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the diagonal piece of wood will act as the hypotenuse of a right triangle, with the sides of the wooden box as the other two sides.
Since the wooden box is a 12-inch square, both of its sides are 12 inches.
Let's denote the length of the diagonal piece as "d".
Using the Pythagorean theorem: d^2 = 12^2 + 12^2
d^2 = 144 + 144
d^2 = 288
d ≈ √288
d ≈ 16.97
The length of the diagonal piece, rounded to the nearest inch, would be 17 inches.