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?

$13$

$30$

$60$

$300$

$1800$

正方形面积给出了三个正方形的边长

The square areas give the side lengths of the three squares.

这些边长形成 $5-12-13$ 直角三角形

The side lengths form a $5-12-13$ right triangle.

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

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

所以正确答案是 B。

The side lengths of the squares are $\sqrt{169} = 13,$ $\sqrt{144} = 12,$ and $\sqrt{25} = 5.$ 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.