Question

一个三角形的边长为 $15$ 、 $20$ 、 $25$ 。求最短高的长度。

The sides of a triangle have lengths of $15,$ $20,$ and $25.$ Find the length of the shortest altitude.

$6$

$12$

$12.5$

$13$

$15$

因为 $15^2+20^2=225+400$ $=625=25^2$ ，这是一个直角三角形，两条直角边为 $15$ 和 $20$ ，面积为 $\dfrac{1}{2}(15)(20)=150$ 。

最短高对应最长边 $25$ ，长度为 $\dfrac{2\cdot 150}{25}=12$ 。

所以正确答案是 B。

Since $15^2+20^2=225+400$ $=625=25^2,$ the triangle is right with legs $15$ and $20,$ and area $\dfrac{1}{2}(15)(20)=150.$

The shortest altitude falls to the longest side $25,$ and equals $\dfrac{2\cdot 150}{25}=12.$

Thus, the correct answer is B.