Question

find the perimeter of the trapezoid. write your answer in simplest form. 2 ft √54 ft √54 ft 2√24 ft

Explanation:

Step1: Simplify the square - root terms

• Simplify \(\sqrt{54}\): \(\sqrt{54}=\sqrt{9\times6}=3\sqrt{6}\)
• Simplify \(2\sqrt{24}\): \(2\sqrt{24}=2\sqrt{4\times6}=2\times2\sqrt{6} = 4\sqrt{6}\)

Step2: Calculate the perimeter

The perimeter \(P\) of a trapezoid is the sum of its side lengths. Let the side lengths be \(a = 2\), \(b=\sqrt{54}\), \(c = 2\sqrt{24}\), \(d=\sqrt{54}\)
\(P=2+\sqrt{54}+2\sqrt{24}+\sqrt{54}\)
Substitute the simplified values:
\(P = 2+3\sqrt{6}+4\sqrt{6}+3\sqrt{6}\)
Combine like terms:
\(P=2+(3\sqrt{6}+4\sqrt{6}+3\sqrt{6})\)
\(P=2 + 10\sqrt{6}\)

Answer:

\(2 + 10\sqrt{6}\text{ ft}\)