Question

A small square, marked X, is cut off from different places from three equal sized sheets as shown in the figure below. In which of them will the perimeter increase?

Answer 1

Solution :-

Let us assume that, the side of each square sheet is 3 unit and a square of 1 unit is cut off from the sheet .

Sheet 1) :-

→ Initial perimeter of sheet = 4a = 4 * 3 = 12 unit .

→ New Perimeter of sheet = 3 + 3 + 2 + 2 + 1 + 1 = 12 unit .

So, Perimeter remains same .

Sheet 2) :-

→ Initial perimeter of sheet = 4a = 4 * 3 = 12 unit .

→ New Perimeter of sheet = 3 + 3 + 2 + 2 + 1 + 1 = 12 unit .

So, Perimeter remains same .

Sheet 3) :-

→ Initial perimeter of sheet = 4a = 4 * 3 = 12 unit .

→ New Perimeter of sheet = 3 + 3 + 3 + 1 + (1 + 1 + 1) + 1 = 14 unit .

So, Perimeter is Increased In sheet 3 .

Hence, Option (C) sheet 3 is correct answer .

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