Final Answer:
A quadrilateral has side lengths of √2√27 inches, √12 inches, 3√3 inches, 2√12 inches. have perimeter is 9√3 + 2√27 in
(option a)
Step-by-step explanation:
To find the perimeter of the quadrilateral, add the lengths of all four sides together. The side lengths given are √2√27 inches, √12 inches, 3√3 inches, and 2√12 inches. Simplify these values where possible: √2√27 = 3√6, √12 = 2√3, and 2√12 = 4√3. Substituting these simplified values, the perimeter simplifies to 9√3 + 2√27 (option a) inches after combining like terms and simplifying the square roots.
Calculating the perimeter involves summing the lengths of all sides of the quadrilateral. Simplifying the square roots to obtain the simplest form of the expression is necessary to find the accurate perimeter measurement.
Understanding how to simplify radicals and add expressions involving square roots is crucial in geometry and algebra, especially when dealing with perimeter, area, or length calculations in shapes with irrational side lengths.