Question

find the perimeter of the trapezoid. the perimeter of the trapezoid is (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Simplify each radical term

• Simplify \(5\sqrt{20}\):

\(5\sqrt{20}=5\sqrt{4\times5}=5\times2\sqrt{5} = 10\sqrt{5}\)

• Simplify \(\sqrt{20}\):

\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\)

• Simplify \(5\sqrt{45}\):

\(5\sqrt{45}=5\sqrt{9\times5}=5\times3\sqrt{5}=15\sqrt{5}\)

Step2: Calculate the perimeter

The perimeter \(P\) of a trapezoid is the sum of its four side - lengths.
\(P = 3\sqrt{5}+5\sqrt{20}+\sqrt{20}+5\sqrt{45}\)
Substitute the simplified radicals:
\(P=3\sqrt{5}+10\sqrt{5}+2\sqrt{5}+15\sqrt{5}\)
Combine like terms: \((3 + 10+2 + 15)\sqrt{5}\)
\(30\sqrt{5}\)

Answer:

\(30\sqrt{5}\text{ in}\)