Question

1. find the perimeter of the triangle below. write in the simplest form.

√12
10√8
5√2

Explanation:

Step1: Simplify square - root terms

Simplify $\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}$, and $10\sqrt{8}=10\sqrt{4\times2}=20\sqrt{2}$.

Step2: Calculate the perimeter

The perimeter $P$ of a triangle is the sum of its side - lengths. So $P = 2\sqrt{3}+20\sqrt{2}+5\sqrt{2}$.

Step3: Combine like terms

Combine the $\sqrt{2}$ terms: $20\sqrt{2}+5\sqrt{2}=(20 + 5)\sqrt{2}=25\sqrt{2}$. So $P=2\sqrt{3}+25\sqrt{2}$.

Answer:

$2\sqrt{3}+25\sqrt{2}$