The volume of the rectangular parallelepiped is 240 cubic meters. cm., the height is 5 cm

The volume of the rectangular parallelepiped is 240 cubic meters. cm., the height is 5 cm, and the length is 2 cm more than the width. Find the length of the box.

Volume – 240 cm ^ 3;

Height – 5 cm;

Width -? cm;

Length -? 2 cm wider.

Decision:

Let us solve this problem through the equation, denoting the required value for x. Let x cm be the length. If the length is 5 cm more than the width, then the width is 2 cm less than it, which means the width is (x – 2) cm.Knowing that the volume of a rectangular parallelepiped is equal to the product of length, height and width, we compose the following equation:

5 * x * (x – 2) = 240;

5x (x – 2) = 240.

Let’s open the brackets according to the distribution law:

5x ^ 2 – 10x = 240;

5x ^ 2 – 10x – 240 = 0;

a = 5; b = -10; c = -240.

D = b ^ 2 – 4ac = (-10) ^ 2 – 4 * 5 * (-240) = 4900.

x1 = (-b + √D) / 2a = (- (- 10) + √4900) / 2 * 5 = 8;

x2 = (-b – √D) / 2a = (- (- 10) – √4900) / 2 * 5 = -6.

The length cannot be negative, so it is 8 cm.

Answer: 8 cm.