What is the longest line segment that can be drawn in a right rectangular prism that is 12 cm long, 11 cm wide, and 9 cm tall.
12.89
To find the longest line segment that can be drawn in a right rectangular prism, we need to find the space diagonal. The space diagonal of a rectangular prism is the longest possible line segment connecting any two opposite corners of the prism.
In this case, the length, width, and height of the rectangular prism are given as 12 cm, 11 cm, and 9 cm respectively.
To find the space diagonal, we can use the Pythagorean theorem, which states that in a right-angled 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.
Thus, the formula to find the space diagonal is:
Space diagonal = √(length^2 + width^2 + height^2)
Substituting the values into the formula, we get:
Space diagonal = √(12^2 + 11^2 + 9^2)
= √(144 + 121 + 81)
= √346
≈ 18.6 cm
Therefore, the longest line segment that can be drawn in the given right rectangular prism is approximately 18.6 cm.
To find the longest line segment that can be drawn in a right rectangular prism, we need to determine the length of the longest diagonal.
In a right rectangular prism, the three dimensions (length, width, and height) form a right triangle. The longest diagonal is the hypotenuse of this right triangle.
We can use the Pythagorean theorem to calculate the length of this diagonal. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, the length of the longest diagonal (c) is the hypotenuse, and the length (a) and width (b) are the other two sides.
So, applying the Pythagorean theorem:
c^2 = a^2 + b^2
In our case, the length is 12 cm, the width is 11 cm, and the height is 9 cm. Plugging these values into the equation:
c^2 = 12^2 + 11^2 + 9^2
c^2 = 144 + 121 + 81
c^2 = 346
Now, to find the length of the longest diagonal (c), we can take the square root of both sides:
c = √346
Using a calculator, we can determine that the square root of 346 is approximately 18.6
Therefore, the longest line segment that can be drawn in this right rectangular prism is approximately 18.6 cm long.