Question

multiple choice 10 points

1. what is the perimeter of a triangle if the side lengths are 2√45, 5√20, and 4√80? (perimeter = the sum of the length of all sides)

11√145 32√5 20√5 32√15
multiple choice 10 points

1. combine these radicals

3√2 - 5√2
-2 -3√2 0 -3√2

Explanation:

Step1: Simplify each radical term

• Simplify $2\sqrt{45}$: $2\sqrt{45}=2\sqrt{9\times5}=2\times3\sqrt{5} = 6\sqrt{5}$.
• Simplify $5\sqrt{20}$: $5\sqrt{20}=5\sqrt{4\times5}=5\times2\sqrt{5}=10\sqrt{5}$.
• Simplify $4\sqrt{80}$: $4\sqrt{80}=4\sqrt{16\times5}=4\times4\sqrt{5}=16\sqrt{5}$.

Step2: Calculate the perimeter

The perimeter $P$ of the triangle is the sum of the side - lengths. So $P=6\sqrt{5}+10\sqrt{5}+16\sqrt{5}=(6 + 10+16)\sqrt{5}=32\sqrt{5}$.

Answer:

$32\sqrt{5}$