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?

Here's a brief explanation for each statement:

Statement 1: It is possible to cut the sheet exactly into 4 square sheets. The rectangular sheet has dimensions 20 cm x 8 cm, so its area is 20 * 8 = 160 sq cm. It is possible to cut the sheet into four square sheets of different sizes:

1. Two squares of 8 cm x 8 cm. Each has an area of 64 sq cm. Total area = 2 * 64 = 128 sq cm.
2. Two squares of 4 cm x 4 cm. Each has an area of 16 sq cm. Total area = 2 * 16 = 32 sq cm. The total area of these four squares is 128 + 32 = 160 sq cm, which matches the area of the original sheet. To cut them: From the 20x8 sheet, cut an 8x8 square from one end. This leaves a 12x8 rectangle. Cut another 8x8 square from the other end of the original sheet (or the remaining 12x8 part). This leaves a 4x8 rectangle in the middle. The 4x8 rectangle can then be cut into two 4x4 squares. Thus, statement 1 is correct.

Statement 2: It is possible to cut the sheet into 10 triangular sheets of equal area. The area of the rectangular sheet is 160 sq cm. If it is cut into 10 triangular sheets of equal area, each triangle must have an area of 160 / 10 = 16 sq cm. This is possible: Divide the 20 cm length of the rectangle into 5 equal segments of 4 cm each. This creates five smaller rectangles, each measuring 4 cm x 8 cm. Each of these 4x8 cm rectangles has an area of 32 sq cm. Each 4x8 cm rectangle can be cut along its diagonal into two triangles. Each of these triangles will have an area of 32 / 2 = 16 sq cm. Since there are 5 such 4x8 cm rectangles, and each yields 2 triangles of 16 sq cm, we get a total of 5 * 2 = 10 triangular sheets, each with an area of 16 sq cm. Thus, statement 2 is correct.

Since both statements 1 and 2 are correct, the answer is C.