AMC 8 1999 Problem 14
AMC8 1999 年第 14 题
四边形与多边形★★★☆☆
In trapezoid , the sides and are equal. The perimeter of is
在梯形 中，边 和 相等。梯形 的周长是
- A.27
- B.30
- C.32
- D.34
- E.48
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
There is a rectangle present, with both horizontal bases being 8 units in length. The excess units on the bottom base must then be 16-8=8. The fact that and are equal in length indicate, by the Pythagorean Theorem, that these excess lengths are equal. There are two with a total length of 8 units, so each is 4 units. The triangle has a hypotenuse of 5, because the triangles are 3-4-5 right triangles. So, the sides of the trapezoid are 8, 5, 16, and 5. Adding those up gives us the perimeter, units.
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