The width of a rectangular parallelepiped is 60% of the length, the height is 20% greater than the width, and the sum

The width of a rectangular parallelepiped is 60% of the length, the height is 20% greater than the width, and the sum of its three dimensions is 5.8 dm. Find the volume and area of the side surface of this parallelepiped

Let us denote the length of the parallelepiped by X.

Then the width will be 0.6x (60% of x).

And the height will be equal to 1.2 * 0.6x = 0.72x.

The sum of the three measurements is 5.8 dm, the equation is obtained:

x + 0.6x + 0.72x = 5.8;

2.32x = 5.8;

x = 5.8 / 2.32 = 2.5 (dm) – we found the length of the parallelepiped.

The width is 0.6x = 0.6 * 2.5 = 1.5 dm.

The height is 1.2 * 1.5 = 1.8 dm.

Let’s calculate the volume of a rectangular parallelepiped:

V = a * b * c;

V = 2.5 * 1.5 * 1.8 = 6.75 cc dm.

Let’s find the area of ​​the lateral surface. It is calculated by the formula S (side) = P (base) * h.

Find the perimeter of the base: (2.5 + 1.5) * 2 = 8 dm.

S (main) = 8 * 1.8 = 144 sq. Dm.

Answer: the volume of the parallelepiped is 6.75 cubic meters. dm. The lateral surface area is 144 sq. dm.