A cube with edges inch long is shown below. What is the length, in inches, of a diagonal that runs from one corner of the cube to the opposite corner?

D^2 = L^2 + W^2 + h^2,

D^2 = 1^2 + 1^2 + 1^2 = 3,
D = 1.732. Inches.

Well, if you ask me, the cube is already pretty edgy on its own! But to answer your question, let's imagine a little adventure. Picture yourself walking from one corner of the cube to the opposite corner. It's like going through a secret tunnel from one side of the cube to the other!

Now, if we use the Pythagorean theorem, which is like the GPS of geometry, we can find the length of that diagonal. The Pythagorean theorem states that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse (or in this case, the diagonal).

In our cube adventure, each side of the cube is 1 inch long, right? So, we have a right-angled triangle where the two shorter sides are 1 inch each. Using the Pythagorean theorem, we can calculate the length of the diagonal:

diagonal^2 = 1^2 + 1^2

diagonal^2 = 1 + 1

diagonal^2 = 2

Therefore, the length of the diagonal, in inches, is the square root of 2. Now, that's a pretty irrational length for a diagonal, but hey, geometry can be a bit quirky sometimes, just like the clown in me!

To find the length of the diagonal that runs from one corner of the cube to the opposite corner, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In the case of a cube, the diagonal that runs from one corner of the cube to the opposite corner forms a right triangle with two sides of equal length, which are the edges of the cube.

Let's call the length of each edge of the cube "x".

According to the Pythagorean theorem, we can write the equation as:

x² + x² = d²

where "x" represents the length of the edge of the cube and "d" represents the length of the diagonal.

Simplifying the equation:

2x² = d²

Taking the square root of both sides:

√(2x²) = √(d²)

√2 * x = d

Therefore, the length of the diagonal is equal to the square root of 2 times the length of the edge of the cube.

In this case, the length of the edge is 1 inch, so we can substitute x = 1 into the equation:

d = √2 * 1

d = √2

Using a calculator, we can approximate the value of √2 as 1.414.

Therefore, the length of the diagonal that runs from one corner of the cube to the opposite corner is approximately 1.414 inches.

12sq feet