A rectangular piece of 20 cm × 15 cm is cut off from a bigger rectang

1.	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» (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.

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»

(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.