Final answer:
To find the length of AC, use the Pythagorean Theorem to solve for the hypotenuse of a right triangle formed by the sides of the square. Substitute the length of one side of the square into the equation and simplify to find the length of AC.
Step-by-step explanation:
To find the length of AC, we can use the Pythagorean Theorem. In a square, the diagonal is equal to the hypotenuse of a right triangle formed by the sides of the square. Let's label the length of one of the sides of the square as x. Then, using the Pythagorean Theorem, we have:
AC^2 = x^2 + x^2
AC^2 = 2x^2
AC = sqrt(2x^2)
Since the side length of the square is given as 21m, we can substitute x = 21m into the equation:
AC = sqrt(2(21m)^2)
AC = sqrt(882m^2)
AC ≈ 29.7m (rounded to the nearest tenth).