The width of the rectangular parallelepiped is greater than one, the length is greater than the height

| May 29, 2021 | education

The width of the rectangular parallelepiped is greater than one, the length is greater than the height and the height is greater than the width. In this case, the length, width and height are natural numbers, and the volume of several such parallelepipeds is 315. Find the surface area of this parallelepiped.

By condition, it is known that the width, length and height of a rectangular parallelepiped are not equal to each other.

The volume of several such parallelepipeds is equal to 315. You can decompose the number 315 into prime factors and choose three unequal natural numbers.

315 = 3 * 3 * 5 * 7.

This means that the width of the rectangular parallelepiped is 3, the height that is greater than the width is 5, and the length, which is greater than the height, is 7.

The surface area of this parallelepiped is

2 * (3 * 5 + 3 * 7 + 5 * 7) = 142



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