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.
5√ 3
3√12
We know that the perimeter of a figure is just the sum of the lengths of its sides. In this case, we have two sides with lengths given in radical form.
Let's start by simplifying 3√12. We can rewrite 12 as 4*3 since 4 is a perfect square.
3√12 = 3√(4*3)
= 3√4 * √3
= 3*2√3
= 6√3
So now we know that one of the sides has a length of 6√3.
Next, let's look at 5√3. This is already in simplified form, so we don't need to do any more work on it.
Now we just need to add the two sides together to get the perimeter.
Perimeter = 6√3 + 5√3
= 11√3
So the perimeter of the figure is 11√3, with units depending on the original measurement (could be inches, centimeters, etc.).