The length of the rectangular parallelepiped is 2 times its width and 3 times its height. Find the sum of the lengths

The length of the rectangular parallelepiped is 2 times its width and 3 times its height. Find the sum of the lengths of the edges of this parallelepiped, if the surface area is 1000 m2?

We introduce the variable x and denote the width of the parallelepiped in this way, then we get:
2x (m) – the length of the parallelepiped;
6x (m) – height.
Let’s use the formula for the surface area of a rectangular parallelepiped and write the equation:
S = 2 * (a * b + b * h + a * h).
2 * (2x * x + x * 6x + 2x * 6x) = 1000;
2x² + 6x² + 12x² = 500;
20x² = 500;
x² = 25;
x = ± √25 = ± 5.
-5 is an extraneous root.
Box edges:
5 (m) – width;
2 * 5 = 10 (m) – length;
6 * 5 = 30 (m) – height.
In total, the parallelepiped has 12 edges, we find the sum of their lengths:
4 * 5 + 4 * 10 + 4 * 30 = 180 (m).
Answer: the sum of the lengths of the edges is 180 m.