In the box shown at the right, what is th length of the dashed line? There is a picture of a cube with a dashed line going through it diagonally. On top of the box a side is marked 12cm, on the side 8cm, and bottom 9cm.
To find the length of the dashed line, we can use the Pythagorean theorem.
The Pythagorean theorem 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 lengths of the other two sides.
In this case, the dashed line represents the hypotenuse of a right triangle inside the cube. We can use the side lengths provided to find the length of the dashed line.
From the side marked 12cm, we can imagine a vertical line going down from the top corner of the cube to meet the dashed line, creating a right triangle with one side of length 8cm and another side of length 9cm.
Using the Pythagorean theorem, we can find the length of the dashed line as follows:
dashed line^2 = 8cm^2 + 9cm^2
dashed line^2 = 64cm^2 + 81cm^2
dashed line^2 = 145cm^2
Taking the square root of both sides, we get:
dashed line = √145cm
So the length of the dashed line in the cube is approximately 12.042 cm (rounded to three decimal places).
To find the length of the dashed line, we need to use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the dashed line as the hypotenuse of a right triangle. The lengths of the other two sides are the edge lengths of the cube.
Let's call the length of the dashed line "d". According to the Pythagorean theorem, we have:
d^2 = (length of one side)^2 + (length of another side)^2
In the given scenario, there are three possible right triangles we can form by considering the sides of the cube. We'll consider the combination where the dashed line is the hypotenuse and the sides adjacent to it are the edges of the cube.
So, let's calculate the length of the dashed line:
d^2 = 12^2 + 8^2
d^2 = 144 + 64
d^2 = 208
To find the length of the dashed line, we take the square root of both sides:
d = √208
d ≈ 14.42 cm
Therefore, the approximate length of the dashed line is 14.42 cm.