a box is in the shape of a cube where each face of the box is 12 inches by 12 inches. How long is the longest possible stick that can fit inside this cube?
Actually, since we have a 3D cube, the longest stick goes from the bottom corner to the opposite top corner.
d^2 = 12^2 + 12^2 + 12^2 = 3*12^2
d = 12√3 = 20.78
This is time for the Pythagorean Theorem.
a^2 + b^2 = c^2
12^2 + 12^2 = c^2
144 + 144 = c^2
288 = c^2
16.97 = c
To find the longest possible stick that can fit inside the cube, we need to find the length of the diagonal of the cube.
The length of each side of the cube is 12 inches. Using the Pythagorean theorem, we can find the length of the diagonal (d) by calculating the square root of the sum of the squares of the 3 sides.
d = √(12^2 + 12^2 + 12^2)
= √(144 + 144 + 144)
= √432
≈ 20.784 inches
Therefore, the longest possible stick that can fit inside the cube is approximately 20.784 inches.
To find the longest possible stick that can fit inside this cube, we need to find the diagonal of the cube, which can be thought of as the longest line segment connecting two nonadjacent corners of the cube.
To find the length of the diagonal, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, each face of the cube is 12 inches by 12 inches, so we can consider one face as the base of the cube. The diagonal of this face can be found using the Pythagorean theorem:
diagonal = sqrt(12^2 + 12^2)
Simplifying this gives us:
diagonal = sqrt(144 + 144)
= sqrt(288)
Since the diagonal is the longest possible stick that can fit inside the cube, the length of the diagonal is the answer to our question.
Therefore, the longest possible stick that can fit inside this cube is sqrt(288) inches.