Find the perimeter of the figure below. Show all work for each step. Work should include explanations in words detailing how you simplify each specific radical. Take your time and be thorough. Include units in final answer. 2√6 and 3√54
First, simplify the radicals:
√6 can't be simplified further, but √54 can be simplified using the prime factorization method:
√54 = √(2 x 3 x 3 x 3) = 3√2 x 3
Next, substitute the simplified radicals into the perimeter formula and simplify:
Perimeter = 2(2√6) + 2(3√2 x 3)
Perimeter = 4√6 + 6√2 x 3
Perimeter = 4√6 + 18√2
Perimeter ≈ 29.17 units (rounded to nearest hundredth)