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Question 17

Isosceles trapezoid $$ABCD$$ has $$AB = 10$$, $$CD = 20$$, $$BC = AD$$, and an area of 180. Then the length of $$BC$$ is ______.


Correct Answer: 13

Solution

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The area gives $$\frac{1}{2}(10 + 20)h = 180$$, so the height is $$h = 12$$. Dropping perpendiculars from $$A$$ and $$B$$ to $$CD$$ leaves $$\frac{20 - 10}{2} = 5$$ on each side. Hence $$BC = \sqrt{12^2 + 5^2} = \sqrt{169} = 13$$.

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