12. A rectangular sheet of paper of length 10 cm and broadth B cm Is cut into two identical pleces along the dotted lines as shown below (Figure 1). The two plocos are then joined to form - now shape (Figure 2). If the helght and width of each step in the new shape are EQUAL, what is the PERIMETER of the new shape in Figure 27 A. 36 cm B. 48 cm C. 52 cm D. 56 cm
Answers
Answer:
Correct option is A)
Area of rectangular sheet = length × breadth
=(20×10) cm
2
=200 cm
2
Area of rectangular piece that is cut from the sheet = length × breadth
=(5×2) cm
2
=10 cm
2
Area of resultant figure = (area of rectangle sheet) – (area of rectangular piece)
=(200−10) cm
2
=190 cm
2
Perimeter of rectangle sheet before piece is cut = 2 (length + breadth)
=2(20+10)
=60 cm
Length of outer boundaries of resultant figure will be 20cm, 8cm, 5cm, 2cm, 15cm and 10cm
Perimeter of resultant figure = sum of all sides of the new figure formed
= (20 + 8 + 5 + 2 + 15 + 10)
= 60 cm
Thus, it can be observed that the perimeter remains the same but area changes.
∴ correct option is (A)
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