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# trapezoid

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The measure of one of the smaller base angles of an isosceles trapezoid is 60 degrees. The shorter base is 5 inches long and the altitude is sqrt(3) inches long. What is the number of inches in the perimeter of the trapezoid?

Jul 4, 2022

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Note that we have a $$30-60-90$$ triangle with the longer leg being $$\sqrt 3$$. This means that the other leg is 1, and the hypotenuse is 2.

This means that the length of the longer base is $$5 + (2 \times 1) = 7$$

So, the total perimeter is $$7 + 5 + (2 \times 2) = \color{brown}\boxed{16}$$

Jul 4, 2022