The length of the rectangular parallelepiped is 5 cm more than the width, the height is 2 cm more than the length, and its volume is 240 cubic cm. What are the sides of this parallelepiped?
So, the length of the rectangular parallelepiped is 5 cm more than the width, the height is 2 cm more than the length, which means the height is 7 cm more than the width (5 + 2), knowing that the volume of the parallelepiped is equal to the height multiplied by the length and multiplied by the width.
Let the width be x, then the length is x + 5, and the height is x + 7, knowing that the volume is 240 cm ^ 3, we will compose and solve the equation:
x * (x + 5) * (x + 7) = 240;
x * (x ^ 2 + 7x + 5x + 35) = 240;
x * (x ^ 2 + 12x + 35) = 240;
x ^ 3 + 12x ^ 2 + 35x = 240;
From this equation it follows that x = 3
Hence, the width is 3cm, the length is 8cm, and the height is 10cm.
Answer: 3cm, 8cm, 10cm.
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