Question

До гіпотенузи прямокутного трикутника проведено висоту і медіану відстань між основами яких 7 см знайдіть площу трикутника якщо медіана проведена до гіпотенузи дорівнює 25 см

Answer 1

На фотографіїї все видно.

Answer 2

Finding the Area of a Right Triangle with a Median and Altitude

To find the area of a right triangle when the median and altitude are drawn from the hypotenuse, we need to use the properties of right triangles and apply some basic geometry principles.

Let's break down the problem step by step:

1. We are given that the distance between the bases of the median and altitude is 7 cm. 2. We are also given that the median drawn to the hypotenuse is 25 cm.

To find the area of the triangle, we need to determine the lengths of the triangle's sides. Let's denote the lengths as follows:

- The length of the median drawn to the hypotenuse: 25 cm. - The length of the altitude: 7 cm. - The length of the base adjacent to the median: x cm. - The length of the other base: y cm.

To solve for the lengths of the bases, we can use the properties of similar triangles. In a right triangle, the median drawn to the hypotenuse divides the hypotenuse into two segments, each of which is equal to half the length of the hypotenuse. Therefore, we can set up the following equation:

x + y = 25

Since the distance between the bases of the median and altitude is 7 cm, we can also set up the following equation:

x - y = 7

Solving these two equations simultaneously will give us the values of x and y.

By adding the two equations together, we get:

2x = 32

Dividing both sides by 2, we find:

x = 16

Substituting the value of x into one of the equations, we can solve for y:

16 + y = 25

y = 9

Now that we have the lengths of the bases, we can calculate the area of the triangle using the formula:

Area = (1/2) * base * height

In this case, the base is y = 9 cm and the height is the altitude, which is given as 7 cm.

Plugging in the values, we get:

Area = (1/2) * 9 * 7 = 31.5 cm²

Therefore, the area of the triangle is 31.5 cm².

Please note that the search results provided by You.com did not contain relevant information for this specific problem. The solution was derived using the properties of right triangles and basic geometry principles.