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

| August 28, 2021 | education

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.



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