Question

В прямоугольный треугольник с катетами 6 см и 10 см вписан имеющий с ним общий угол прямоугольник наибольшей площади. Найти площадь прямоугольника. (Решать через функцию)

Answer 1

Я не знаю правельної відповіді, походу її немає!

Answer 2

Finding the Area of the Rectangle Inscribed in a Right Triangle

To find the area of the rectangle inscribed in a right triangle, we can use the following steps:

1. Determine the lengths of the two legs (or catheti) of the right triangle. In this case, the lengths are given as 6 cm and 10 cm.

2. Identify the right angle in the triangle. This angle is common to both the triangle and the inscribed rectangle.

3. The rectangle with the largest area that can be inscribed in a right triangle is a square. Therefore, we need to find the length of one side of the square.

4. To find the length of one side of the square, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, the hypotenuse of the right triangle is the side of the square, and the two legs are the other two sides. Let's denote the length of the side of the square as s.

Using the Pythagorean theorem, we have:

s^2 = 6^2 + 10^2

Solving this equation, we find:

s^2 = 36 + 100

s^2 = 136

Taking the square root of both sides, we get:

s = √136

5. Now that we have the length of one side of the square, we can find the area of the square (which is also the area of the rectangle) by