Question 1: Calculate the perimeter of a rectangle with a length of 8 cm and a width of 5 cm.

Answer: 26

Question 2: A rectangle has a perimeter of 24 cm. If its length is 7 cm, what is its width?

Answer: 5

Question 3: Construct a rectangle with a perimeter of 20 cm, where the length is 6 cm. Draw and label the rectangle on the grid.

Answer: length 6 cm, width 4 cm

Question 4: Identify and correct the mistake in the following calculation: Perimeter = 2 x (length + width) = 2 x (7 cm + 3 cm) = 20 cm.

Answer: The mistake is in the calculation: 2 x (7 + 3) = 20; actually, 2 x 10 = 20, so the perimeter is 20 cm, which is correct. But if the student mistakenly calculated 2 x (7 + 3) as 23, then they should realize the correct perimeter is 20 cm.

Question 5: Plot the graph of y=2x for x values from 0 to 10 on the grid.

Answer: Points (0,0) to (10,20)

Question 6: A rectangle's length is twice its width. If the perimeter is 36 cm, find the dimensions of the rectangle.

Answer: length 12 cm, width 6 cm

Question 7: A student mistakenly used the formula Perimeter = length + width instead of 2 x (length + width). How does this affect their answer? Explain briefly.

Answer: They would get only half the correct perimeter, leading to an incorrect, smaller value.

Question 8: Given a rectangle with length 10 cm and width 4 cm, what is the error if someone calculates the perimeter as 10 + 4 = 14 cm?

Answer: They forgot to multiply by 2; the correct perimeter is 2 x (10 + 4) = 28 cm.

Question 9: Challenge: Derive the formula for the perimeter of a rectangle using algebra and explain each step briefly.

Answer: Perimeter = sum of all sides. Since opposite sides are equal, perimeter = 2 x (length + width).

Question 10: Identify the common mistake in calculating the perimeter: Using the formula Perimeter = 2 x length + width.

Answer: The mistake is missing parentheses; the correct formula is 2 x (length + width).