find the perimeter of the quadrilateral in simplest form\n2√27 in.\n2√12 in.\n√12 in.\n3√3 in.\n(9√3 + 2√27)…

find the perimeter of the quadrilateral in simplest form\n2√27 in.\n2√12 in.\n√12 in.\n3√3 in.\n(9√3 + 2√27) in.\n(3√12 + 3√3 + 2√27) in.\n15√3 in.\n33√3 in.\ndone

find the perimeter of the quadrilateral in simplest form\n2√27 in.\n2√12 in.\n√12 in.\n3√3 in.\n(9√3 + 2√27) in.\n(3√12 + 3√3 + 2√27) in.\n15√3 in.\n33√3 in.\ndone

Answer

Explanation:

Step1: Simplify square - root terms

Simplify $\sqrt{12}$ and $\sqrt{27}$. We know that $\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}$ and $\sqrt{27}=\sqrt{9\times3}=3\sqrt{3}$.

Step2: Calculate the perimeter

The perimeter $P$ of the quadrilateral is the sum of its side - lengths. $P = 2\sqrt{12}+\sqrt{12}+3\sqrt{3}+2\sqrt{27}$. Substitute $\sqrt{12}=2\sqrt{3}$ and $\sqrt{27}=3\sqrt{3}$ into the above formula: $P=2\times2\sqrt{3}+2\sqrt{3}+3\sqrt{3}+2\times3\sqrt{3}$. $P = 4\sqrt{3}+2\sqrt{3}+3\sqrt{3}+6\sqrt{3}$.

Step3: Combine like terms

$P=(4 + 2+3 + 6)\sqrt{3}=15\sqrt{3}$ in.

Answer:

$15\sqrt{3}$ in.