Respuesta :
Answer:
[tex]\sqrt{3^{3/2}}$ or 2.28 $ Inches[/tex]
Step-by-step explanation:
Side Length of the Cube[tex]=\sqrt{3} \:Inches[/tex]
Diagonal of a face of the cube[tex]=\sqrt{6} \:Inches[/tex]
The diagonal of a cube is determined using the formula:
Length of Diagonal [tex]=\sqrt{3s} ,$ (s=side length of the cube)[/tex]
Therefore, length of the needle [tex]=\sqrt{3\sqrt{3}}[/tex]
[tex]=\sqrt{3*3^{1/2}}\\=\sqrt{3^{1+1/2}}\\=\sqrt{3^{3/2}}\\=2.28 $ Inches[/tex]
Length of the needle =[tex]\sqrt{3^{3/2}}$ or 2.28 $ Inches[/tex]
Pythagoras' theorem, is a basic relationship between the three sides of a right triangle. The length of the needle is 3 inches.
What is Pythagoras theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Given the length of the side of the clear cube is √3, while the length of the diagonal of the cube face is √6, therefore,
The length of the needle = √{(√3)² + (√6)²] = √(3+6) = 3 inches
Hence, the length of the needle is 3 inches.
Learn more about Pythagoras' Theorem:
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