# Two edges of a rectangular parallelepiped extending from one vertex are equal to 2 and 6.

**Two edges of a rectangular parallelepiped extending from one vertex are equal to 2 and 6. The surface area of this parallelepiped is 136 find the third edge.**

1. Let the length of the third edge of the parallelepiped be x.

2. It is known that the surface area of a rectangular parallelepiped is equal to twice the sum of the areas of the three faces of this parallelepiped. Let’s find the areas of the faces of this parallelepiped:

1) the area of the face formed by edges 2 and 6 is 2 * 6 = 12;

2) the area of the face formed by the edges 2 and x is equal to 2 * x;

3) the area of the face formed by the edges 6 and x is 6 * x;

3. Then we write the equality:

2 * (12 + 2 * x + 6 * x) = 136;

12 + 8 * x = 68;

8 * x = 56;

x = 56/8 = 7;

Answer: The length of the third edge is 7.