OA Explanation

Perimeter of ABC = \(15 + x\)
Perimeter of DEF = \(15 + y\)

In a triangle, any side must be less than the sum of other 2 sides and at the same time, greater than the positive difference between them.

\(10 - 5 < x < 10 + 5\)
\(5 < x < 15\)

\(10 - 5 < y < 10 + 5\)
\(5 < y < 15\)

Let us assume that Perimeter or ABC > Perimeter of DEF
So, Maximum possible integer difference = \( x - y\)

Therefore, we must put maximum value for \(x\) and least value for \(y\)

NOTE: The difference of Perimeters must be an integer, that doesn't mean the sides must be an integer value too!

To get an integer value, Maximum value of \(x = 14.5\) and Minimum value of \(y = 5.5\)

i.e. \(14.5 - 5.5 = 9\)

Col. A = Col. B

Hence, option C