Did you know?
Did you know that to find the perimeter of a figure, you need to add up all the sides? In this problem, we are given the lengths of two sides: 2√6 ft and 3√54 ft.
To simplify the first side, 2√6 ft, we can start by breaking down 6 into its prime factors. Since the factors of 6 are 2 and 3, we can rewrite 2√6 ft as 2√(2*3) ft. Taking the square root of 2 gives us √2, so the simplified form becomes 2√2√3 ft. Multiplying 2√2√3 ft, we get 2√6 ft.
Now, let's simplify the second side, 3√54 ft. Similarly, we can break down 54 into its prime factors, which are 2, 3, and 3. So, 3√54 ft can be written as 3√(2*3*3) ft. Taking the square root of 2 gives us √2, and the simplified form becomes 3√2√3√3 ft. Multiplying 3√2√3√3 ft, we get 3√54 ft.
To find the perimeter, we add both sides together: 2√6 ft + 3√54 ft. However, we cannot combine these radicals because their radicands are different. So, the final answer is 2√6 ft + 3√54 ft, in the respective units.
