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

Answer 1

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.