In a rectangular parallelepiped, the length is 3 cm longer than the width and 3 cm less than the height.

In a rectangular parallelepiped, the length is 3 cm longer than the width and 3 cm less than the height. Find the measurements of a rectangular parallelepiped if its surface area is 198 cm2.

Let’s take the width of the parallelepiped for x, then:

x + 3 – its length;

(x + 3) + 3 = x + 6 – height;

x * (x + 3) – base area;

x * (x + 6) – area of one of the faces;

(x + 3) * (x + 6) – the area is different.

We get the equation:

2 * (x ^ 2 + 3x + x ^ 2 + 6x + x ^ 2 + 6x + 3x + 3) = 198;

3x ^ 2 + 18x + 3 = 99;

x ^ 2 + 2x – 30 = 0.

x12 = (-2 + -√ (4 – 4 * (-30)) / 2 = -1 + – 4;

x1 = -1 + 4 = 3; x2 = -1 – 4 = -5 – the root has no physical meaning.

Then the length is:

3 + 3 = 6.

Height:

3 + 6 = 9.

Answer: 3, 6 and 9 cm.