Questions: Find the perimeter of the quadrilateral in simplest form (9 sqrt(3)+2 sqrt(27)) in. (3 sqrt(12)+3 sqrt(3)+2 sqrt(27)) in 15 sqrt(3) in. 33 sqrt(3) in.

Solution Steps

The sides of the quadrilateral are given as:

• \(2\sqrt{27}\) inches
• \(2\sqrt{12}\) inches
• \(\sqrt{12}\) inches
• \(3\sqrt{3}\) inches

Simplify each square root:

• \(2\sqrt{27} = 2 \times \sqrt{9 \times 3} = 2 \times 3\sqrt{3} = 6\sqrt{3}\)
• \(2\sqrt{12} = 2 \times \sqrt{4 \times 3} = 2 \times 2\sqrt{3} = 4\sqrt{3}\)
• \(\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}\)
• \(3\sqrt{3}\) is already simplified

Add the simplified lengths to find the perimeter:

• \(6\sqrt{3} + 4\sqrt{3} + 2\sqrt{3} + 3\sqrt{3}\)

Combine like terms:

• \(6\sqrt{3} + 4\sqrt{3} + 2\sqrt{3} + 3\sqrt{3} = (6 + 4 + 2 + 3)\sqrt{3} = 15\sqrt{3}\)

Final Answer