Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm: 1. It…
Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm:
1. It is possible to cut the sheet exactly into 4 square sheets.
2. It is possible to cut the sheet into 10 triangular sheets of equal area.
Which of the above statements is/are correct?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Solution
Statement 1 is correct: the 20 cm x 8 cm sheet can be cut into squares of 8x8, 8x8 and the remaining 4x8 region into two 4x4 squares - four squares in all (they need not be equal). Statement 2 is correct: the sheet can be divided into 5 strips of 4 cm x 8 cm and each strip cut diagonally into 2 equal triangles, giving 10 triangles of equal area. Hence both statements are correct.