The width of the rectangle of the parallelepiped is 2.5 times its height and 3.5 times shorter than its length.

The width of the rectangle of the parallelepiped is 2.5 times its height and 3.5 times shorter than its length. The sum of the lengths of the edges of the parallelepiped is 1m 96cm. Find its height, width and length in centimeters by making an equation.

The solution of the problem:

1) Given a rectangular parallelepiped with sides:

a – width, b – length, c – height.

2) By condition, c = 2.5a, a = 3.5b, whence we find:

c = 2.5a = 2.5 * 3.5b = 8.75b.

2) The sum of the lengths of the edges of the parallelepiped is known – 1 m 96 cm (196 cm), so we make the equation:

4 (a + b + c) = 196, we substitute the values for a and c, we get an equation with one unknown b:

4 (2.5b + b + 8.75b) = 196, {divide both sides of the equation by 4},

12.25b = 49,

b = 4 (cm).

3) Find a and c:

a = 3.5b = 3.5 * 4 = 14 (cm),

s = 2.5 * 14 = 35 (cm).

Answer: 4cm, 14cm and 35cm.