# The length of a rectangular parallelepiped is 40% longer than its width, and its width is 5 times less than its height.

August 27, 2021 | education

| **The length of a rectangular parallelepiped is 40% longer than its width, and its width is 5 times less than its height. What is the total surface area of a parallelepiped if its volume is 56 dm3?**

Let’s designate the width of the parallelepiped as “x” dm, then taking into account the condition of the problem, its length will be “x + 0.4x” dm, and the height will be equal to “5x” dm.

Let’s make an equation taking into account that the volume of this parallelepiped is 56 dm³.

x * 1.4x * 5x = 56;

1.4x² * 5x = 56;

7x³ = 56;

x³ = 56/7;

x³ = 8;

x = ³√8 = 2 dm width.

1.4 * 2 = 2.8 dm length.

5 * 2 = 10 dm height.

Let’s calculate the total surface area:

S = 2 * (a * b + b * c + a * c) = 2 * (2.8 * 2 + 2 * 10 + 2.8 * 10) = 2 * (5.6 + 20 + 28) = 107.2 dm².

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