Final answer:
The length of the diagonal bar is 2√11600 cm in surd form.
Step-by-step explanation:
To find the length of the diagonal bar, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal bar) is equal to the sum of the squares of the lengths of the other two sides. In this case, one side of the triangle is the height of the gate (80 cm) and the other side is the width of the gate (2 m = 200 cm). Let's calculate:
Length of the diagonal bar:
c² = a² + b²
c² = 80² + 200²
c² = 6400 + 40000
c² = 46400
c = √46400
c = 2√11600
Therefore, the length of the diagonal bar is 2√11600 cm in surd form.