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The area of a trapezoid is $80$. The length of one base is $4$ units greater than the other base, and the height of the trapezoid is $12$. Find the perimeter of the trapezoid.

 Jan 15, 2024
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We set the smaller base to x, so the area of the trapezoid is

\(12x+24 = 80\)

\(12x = 56\)

\(x = \frac{19}{3}\)

Next, we find the diagonals by using pythagorean theorum.

a = 2

b = 12

c = \(\sqrt{148}\) = \(2\sqrt{39}\)

so the perimeter is 2x+4+2c = 38/3 + 4 + 4 root 39, or \(\frac{50}{3}+4\sqrt{39}\)

 Jan 16, 2024

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