Question

find the perimeter of the rectangle below.

Explanation:

Step1: Simplify \(\sqrt{27}\)

$$\begin{align*} \sqrt{27}&=\sqrt{9\times3}\\ &=\sqrt{9}\times\sqrt{3}\\ & = 3\sqrt{3} \end{align*}$$

Step2: Use the perimeter formula \(P = 2(l + w)\) for a rectangle

Let \(l=3\sqrt{3}\) (simplified \(BC\)) and \(w = 2\sqrt{3}\) (\(DC\)).

$$\begin{align*} P&=2(3\sqrt{3}+2\sqrt{3})\\ &=2\times(5\sqrt{3})\\ &=10\sqrt{3} \end{align*}$$

Answer:

\(10\sqrt{3}\)