Question

В прямоугольном треугольнике катеты равны 13 см и 5 см. Найти высоту опущенную на гипотенузу ПОМОГИТЕ ПОЖАЛУЙСТА ДАНО РЕШЕНИЕ РИСУНОК

Answer 1

Вроде так. У меня только корень не получилось извлечь.

Answer 2

Problem Analysis

We are given a right triangle with two sides, or catheti, measuring 13 cm and 5 cm. We need to find the length of the altitude dropped onto the hypotenuse.

Solution

To find the length of the altitude dropped onto the hypotenuse, we can use the formula for the area of a triangle. The area of a triangle can be calculated using the formula:

Area = (1/2) * base * height

In this case, the base of the triangle is the length of one of the catheti, and the height is the length of the altitude dropped onto the hypotenuse.

Let's calculate the area of the triangle using the given information:

Area = (1/2) * 5 cm * height

Now, we need to find the length of the hypotenuse. We can use the Pythagorean theorem, which 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.

Let's calculate the length of the hypotenuse using the Pythagorean theorem:

hypotenuse^2 = 13 cm^2 + 5 cm^2

Once we have the length of the hypotenuse, we can substitute it into the formula for the area of the triangle to solve for the height:

Area = (1/2) * 5 cm * height

Now, let's solve for the height.

Calculation

Using the Pythagorean theorem, we can calculate the length of the hypotenuse:

hypotenuse^2 = 13 cm^2 + 5 cm^2

hypotenuse^2 = 169 cm^2 + 25 cm^2

hypotenuse^2 = 194 cm^2

Taking the square root of both sides, we find:

hypotenuse = sqrt(194) cm

Now, substituting the length of the hypotenuse into the formula for the area of the triangle, we can solve for the height:

Area = (1/2) * 5 cm * height

Area = (1/2) * 5 cm * height

Area = 2.5 cm * height

Since the area of the triangle is equal to the area calculated using the lengths of the catheti, we can equate the two expressions:

2.5 cm * height = (1/2) * 13 cm * 5 cm

2.5 cm * height = 32.5 cm^2

Solving for the height, we find:

height = 32.5 cm^2 / 2.5 cm

height = 13 cm

Therefore, the length of the altitude dropped onto the hypotenuse is 13 cm.

Answer

The length of the altitude dropped onto the hypotenuse in the given right triangle is 13 cm.

Diagram

Unfortunately, I am unable to provide a diagram in this text-based format. However, you can visualize the right triangle with the given catheti of 13 cm and 5 cm, and the altitude dropped onto the hypotenuse as a line segment perpendicular to the hypotenuse.