Final answer:
a) The equation to find the area of a square is A = x^2. b) To solve the equation, substitute x and calculate A. then A = (3.5)^2 = 12.25 square meters. c) The equation to find the perimeter of a square is P = 4x. d) Solve the equation for P. P = 4 * 3.5 = 14 meters. e) Prove that the area of the circle is not 12.25m². The student in grade eight is incorrect, as 12.6 is actually greater than 12.63.
Step-by-step explanation:
a) The equation to find the area of a square with side length x is A = x^2.
b) To solve the equation A = x^2, given that x is the length of one side of the square, we can substitute the given value of x and calculate the value of A. For example, if x = 3.5 meters, then A = (3.5)^2 = 12.25 square meters.
c) The equation to find the perimeter of a square with side length x is P = 4x.
d) To solve the equation P = 4x, given that x is the length of one side of the square, we can substitute the given value of x and calculate the value of P. For example, if x = 3.5 meters, then P = 4 * 3.5 = 14 meters.
e) To prove that the area of the circle is 12.25m², we need to calculate the area of a circle with a diameter of 4 meters. The formula for the area of a circle is A = πr^2, where r is the radius. Since the diameter is 4 meters, the radius is 2 meters. Substituting this value into the formula, we get A = π(2^2) = 4π ≈ 12.57 square meters. As the area of the circle is approximately 12.57 square meters, it is not equal to 12.25m² and therefore cannot be proven to be 12.25m².
The student in grade eight who says that 12.6 is less than 12.63 is incorrect. The number 12.6 is actually greater than 12.63. The digit 6 in 12.6 is larger than the digit 3 in 12.63, so 12.6 is greater than 12.63.