Question

A rectangular piece of 20 cm × 15 cm is cut off from a bigger rectangle as shown in the figures below. In each case, find the difference is perimeter before and after the piece is cut off.

Answer 1

(i) Perimeter of square (when rectangular piece cut off) = 80 + 80 + 30 + 15 + 20 + 15 + 30 + 80 = 350 cm 

Perimeter of complete square = 4 (80) = 320 cm 

∵ 350 > 320 

∴ Perimeter will be increased. 

Thus, increment in perimeter = 350 – 320 = 30 cm 

(ii) Initial perimeter of square = 4 (60) = 240 cm 

Perimeter, after piece cut off = 60 + 60 + 45 + 20 + 15 + 40 

= 60 + 60 + (45 + 15) + (20 + 40) = 60 + 60 + 60 + 60 = 240 

∵ 240 = 240 

Thus, no change in perimeter of square.