# V.I. Arnold says Russian students can’t solve this problem, but American students can — why?

In a book of word problems by V.I Arnold, the following appears:

1. The hypotenuse of a right-angled triangle (in a standard American examination) is 10 inches, the altitude dropped onto it is 6 inches. Find the area of the triangle.

American school students had been coping successfully with this problem for over a decade. But then Russian school students arrived from Moscow, and none of them was able to solve it as had their American peers (giving 30 square inches as the answer). Why?

Here‘s the book. I assume the answer is some joke at the expense of the Americans, but I don’t get it. Possibly a joke about inches? Anyone?

## Answer

There is no such right triangle. The maximum possible altitude is half the hypotenuse (inscribe the triangle into a circle to see this), which here is $5$ inches. You would only get $30$ square inches if you tried to compute the area without checking whether the triangle actually exists.

Attribution
Source : Link , Question Author : Eli Rose , Answer Author : Qiaochu Yuan