# In a rectangular parallelepiped, the length is 5 cm longer than the width and 5 cm less than the height.

August 29, 2021 | education

| **In a rectangular parallelepiped, the length is 5 cm longer than the width and 5 cm less than the height. Find the measurements of a rectangular parallelepiped if its surface area is 244 cm2.**

Let the length in a rectangular parallelepiped be a = x cm, then if it is 5 cm greater than the width b, then the width is b = x – 5 cm. Also, the length is 5 cm less than the height c, which means the height is c = x + 5 cm.

The surface area of a rectangular parallelepiped can be calculated as

S = 2 ab + 2 bc + 2 ac.

If the surface area of a rectangular parallelepiped is 244 cm ^ 2, then

244 = 2 x * (x – 5) + 2 (x + 5) * (x – 5) + 2 x * (x + 5),

where

6 x ^ 2 = 294

and x ^ 2 = 49.

a = 7 cm, b = 2 cm, c = 12 cm.

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