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?

The correct option is Both 1 and 2.

Let us analyze each statement step-by-step to understand why both are correct.

Analysis of Statement 1: It is possible to cut the sheet exactly into 4 square sheets.
We are given a rectangular sheet with length 20 cm and breadth 8 cm. The total area of this sheet is:
Area = length × breadth = 20 cm × 8 cm = 160 cm².
If we want to cut it exactly into 4 square sheets, we don't necessarily have to make all 4 squares equal in size. Let's see if we can cut it into 4 squares (of potentially different sizes) without any wastage.
1. First, we can cut a square of side 8 cm from one end of the 20 cm × 8 cm rectangle. This leaves a rectangle of dimensions (20 - 8) cm × 8 cm, which is 12 cm × 8 cm.
2. From this remaining 12 cm × 8 cm rectangle, we can cut another square of side 8 cm. This leaves a rectangle of dimensions (12 - 8) cm × 8 cm, which is 4 cm × 8 cm.
3. Now, we have a rectangle of dimensions 8 cm × 4 cm. We can cut this rectangle exactly into two equal squares, each having a side of 4 cm (since 8 cm can be divided into two 4 cm segments).
Thus, we have successfully cut the rectangular sheet into exactly 4 square sheets: two squares of side 8 cm (each with area 64 cm²) and two squares of side 4 cm (each with area 16 cm²).
Total area of the 4 squares = 64 + 64 + 16 + 16 = 160 cm², which matches the original area of the sheet exactly. Hence, Statement 1 is correct.

Analysis of Statement 2: It is possible to cut the sheet into 10 triangular sheets of equal area.
The total area of the sheet is 160 cm². If we cut it into 10 triangular sheets of equal area, the area of each triangle must be:
Area of each triangle = 160 cm² / 10 = 16 cm².
We can achieve this by dividing the rectangular sheet using a simple grid layout:
1. Divide the length (20 cm) into 5 equal parts, each of width 4 cm (since 20 / 5 = 4).
2. Keep the breadth as 8 cm. This divides the original rectangle into 5 smaller rectangles, each of dimensions 4 cm × 8 cm.
3. Cut each of these 5 smaller rectangles diagonally into 2 triangles. Since a diagonal cuts a rectangle into two triangles of equal area, each triangle will have:
Area = (1/2) × base × height = (1/2) × 4 cm × 8 cm = 16 cm².
Since we have 5 such rectangles and each yields 2 triangles, we get a total of 5 × 2 = 10 triangles of equal area (16 cm² each) without any wastage. Hence, Statement 2 is also correct.

Since both Statement 1 and Statement 2 are correct, the correct answer is indeed Both 1 and 2.