Question

Решите пожалуйста У треугольника со сторонами 4 и 16 проведены высоты к этим сторонам. Высота, проведенная к первой стороне, равна 4. Чему равна высота, проведенная ко второй стороне?

Answer 1

Сама долго вчера думала, и вдруг вспомнила про площади! :

Answer 2

I will try to answer your question in detail. Please solve the following problem: A triangle has sides of 4 and 16. The heights to these sides are drawn. The height to the first side is 4. What is the height to the second side?

Solution:

Let the triangle be ABC, where AB = 4, AC = 16, and BD and CE are the heights to these sides. Let BD = 4 and CE = x. Then, by the Pythagorean theorem, we have:

AD^2 + BD^2 = AB^2 CD^2 + CE^2 = AC^2

Solving for AD and CD, we get:

AD = sqrt(AB^2 - BD^2) = sqrt(4^2 - 4^2) = 0 CD = sqrt(AC^2 - CE^2) = sqrt(16^2 - x^2)

Now, the area of the triangle ABC can be expressed in two ways:

Area = (1/2) * AB * BD = (1/2) * AC * CE Area = (1/2) * 4 * 4 = (1/2) * 16 * x

Simplifying and solving for x, we get:

x = 1

Therefore, the height to the second side is 1.

You can also find similar problems and solutions on the web, such as [this one](https://ege.sdamgia.ru/problem?id=56767).