Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm:

Correct Option (B)

Statement 2 is correct.

• The total area of the rectangular sheet is calculated as length × breadth = 20 cm × 8 cm = 160 cm².
• If the sheet is to be cut into 10 triangular sheets of equal area, each triangle must possess an area of 160 cm² / 10 = 16 cm².
• Consider dividing the length of the rectangle (20 cm) into 5 equal segments, each measuring 4 cm. This operation creates 5 smaller rectangles, each having dimensions of 8 cm (breadth) × 4 cm (length).
• Each of these 5 smaller 8 cm × 4 cm rectangles can be precisely divided into two triangles of equal area by drawing a diagonal. For such a triangle, if 4 cm is considered the base and 8 cm the height, its area is (1/2) × base × height = (1/2) × 4 cm × 8 cm = 16 cm².
• Since 5 such smaller rectangles yield a total of 10 triangles, each with an area of 16 cm², it is demonstrably possible to cut the sheet into 10 triangular sheets of equal area.

Incorrect Options:

Statement 1 is incorrect.

• The total area of the rectangular sheet is 160 cm².
• If the sheet were to be cut exactly into 4 square sheets of equal area, each square would necessarily have an area of 160 cm² / 4 = 40 cm².
• The side length of such a square would be √(40) cm.
• For a rectangular sheet to be cut exactly into smaller square sheets using standard straight cuts, the side length of the squares must be a rational number that allows for precise division of the original sheet's dimensions without any waste or leftover material.
• Since √(40) is an irrational number, it is not possible to cut the 20 cm × 8 cm rectangular sheet into 4 squares with side length √(40) cm in a manner that aligns with typical geometric cutting procedures for such problems.