Measurements of a rectangular parallelepiped 6,4,12. find the diagonal.

At the base of a rectangular parallelepiped is a rectangle. Let 6 be the length of the rectangle and 4 the width of the rectangle. All corners of a rectangle are straight, we find the diagonal of the base of the parallelepiped (the diagonal of the rectangle) according to the Pythagorean theorem:

√ (6² + 4²) = √ (36 + 16) = √56.

If the sides of the base of the box are 6 and 4, then 12 is the height of the box. The height of the box, the diagonal of the base, and the diagonal of the box make up a rectangular triangle (since the height is perpendicular to the base). Find the length of the diagonal of the parallelepiped using the Pythagorean theorem:

√ ((√56) ² + 12²) = √ (56 + 144) = √196 = 14.

Answer: The diagonal of the parallelepiped is 14.

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