The trapezoid shown has a height of length 12 cm, a base of length 16 cm, and an area of 180 cm^2. What is the perimeter of the trapezoid?
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The answer is 43 + sqrt(145).
The answer might be wrong because it just looks suspicious... that radical is sus.
12 * 16 = 192,
192 - 180 = 12. This is the area of the triangular side of the trapezoid.
This means we can find the base of the triangle: 12 / 12 = 1.
And now we can find the top: 16 - 1 = 15.
15 + 16 + 12 + sqrt(145) = 43 + sqrt(145). You cannot simplify sqrt(145).