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A square handkerchief of width 20 cm is cut off from a piece of square cloth 80 cm wide. What will be the change in the perimeter of the cloth if 

(i) The handkerchief is cut off from a corner of the cloth. (figure (i)) 

(ii) The handkerchief is cut off from the middle of a side. (figure (ii))

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Best answer

Perimeter of square piece of cloth initially, 

= 2 (l + b) = 2 (80 + 80) 

= 2 (160) = 320 cm 

(i) There will be no change in perimeter if we cut handkerchief like this figure, because after cutting the handkerchief two sides less and two new sides forms of same size. i.e. equal sides removed and formed. 

(ii) New perimeter in this figure is as below 

Perimeter = 80 + 80 + 80 + 30 + 20 +20+20 + 30 = 240 + 120 = 360 cm In this case, perimeter increased, because after cutting the handkerchief, one side of 20 cm less from a side and three new sides of 20 cm each forms their.

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