QQuestion
If x be the number of edges of a parallelepiped and y be the number of surfaces then for what least value of a, (x + y + a) is a perfect square?
WBBSEClass 10MathematicsRectangular Parallelopiped or Cuboid02 Mark2025 Easy
✓Answer
A parallelepiped has 12 edges and 6 faces
so x + y = 12 + 6 = 18.
We need the smallest positive integer a such that 18 + a is a perfect square.
The next perfect square after 18 is 25,
so a = 25 – 18 = 7.
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