AMC8 1999

AMC8 1999 · Q14

AMC8 1999 · Q14. It mainly tests Pythagorean theorem, Area & perimeter.

In trapezoid ABCD, the sides AB and CD are equal. The perimeter of ABCD is

梯形ABCD中，边AB和CD相等。ABCD的周长是

(A) 27 27

(B) 30 30

(D) 34 34

(E) 48 48

Answer

Correct choice: (D)

正确答案：（D）

Solution

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 $AB$ and $CD$ 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, $8 + 5 + 16 + 5 = 13 + 21 = \boxed{\text{(D)}\ 34}$ units.

有一个矩形，两个水平底边长均为8单位。底边多出的单位数为$16-8=8$。AB和CD等长表明，根据勾股定理，这些多出长度相等。两个共8单位，所以每个4单位。三角形斜边为5，因为是3-4-5直角三角形。因此，梯形边长为8、5、16和5。周长为$8 + 5 + 16 + 5 = 13 + 21 = \boxed{\text{(D)}\ 34}$单位。

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