Question

根据图中三个正方形的面积，内部三角形的面积是多少？

Given the areas of the three squares in the figure, what is the area of the interior triangle?

$13$

$30$

$60$

$300$

$1800$

答案：B

知识点：勾股数三角形面积

难度评级：920

解答：

三个正方形的边长分别为这些长度构成一个勾股数组。 $\sqrt{169} = 13$ $\sqrt{144} = 12,$ $\sqrt{25} = 5.$

因此内部三角形是直角三角形，面积为 $\dfrac{1}{2} \cdot 5 \cdot 12 = 30.$

所以正确答案是 B。

We get that the side lengths of the squares are $\sqrt{169} = 13$ $\sqrt{144} = 12,$ $\sqrt{25} = 5.$ respectively. Note that these lengths form a Pythagorean triple.

Therefore, the interior triangle is right. Its area is $\dfrac{1}{2} \cdot 5 \cdot 12 = 30.$

Thus, B is the correct answer.

2003 AMC 8 第 6 题

答案：B

难度评级：920

解答：

其他年份的第 6 题