The volume of a rectangular parallelepiped is 144 cm ^ 3, the lateral surface area is 144 cm ^ 2

The volume of a rectangular parallelepiped is 144 cm ^ 3, the lateral surface area is 144 cm ^ 2, and the total surface area is 180 cm ^ 2. Find the height of the box.

1. We take the length of the parallelepiped for x, for the width, for the height for z.

2. We compose 3 equations (a, b, c) and solve them:

a) xyz = 144;

b) 2xz + 2yz = 144; 2 (xz + yz) = 144; xz + yz = 72;

c) 2xz + 2yz + 2xy = 180;

xz + yz + xy = 90; We substitute in this equation the obtained value (xz + yz) = 72

72 + xy = 90;

xy = 18. Substitute the resulting xy value into the first equation:

18z = 144.

z = 8.

Answer: the height of the parallelepiped is 8 cm.