AMC 8 2024 Problem 24

AMC8 2024 年第 24

面积与周长(综合)★★★★
Jean made a piece of stained glass art in the shape of two mountains, as shown in the figure below.
One mountain peak is 8 feet high and the other peak is 12 feet high. Each peak forms a 90° angle, and the straight sides of the mountains form 45° angles with the ground.
The artwork has an area of 183 square feet. The sides of the mountains meet at an intersection point near the center of the artwork, h feet above the ground.
What is the value of h?
Jean制作了一件两座山形状的彩色玻璃艺术品,如下图所示。一座山峰高8英尺,另一座山峰高12英尺。每座山的顶部都形成一个90°的角,两座山的直边都与地面形成一个45°的夹角。这件艺术品的面积为183平方英尺。两座山的另一边在艺术品中心附近的位置相交,相交点距离地面h英尺。请问h的值是多少?
AMC 8 2024 Problem 24 figure
  1. A.4
  2. B.5
  3. C.424\sqrt{2}
  4. D.6
  5. E.525\sqrt{2}

正确答案 · Correct Answer

B

解析 · Solution

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