Question

Висота , проведена до гіпотенузи прямокутного трикутника , ділить її на відрізки у відношенні 9: 16 . Менший катет дорівнює 45 см. Знайдіть площу трикутника.

Answer 1

1) Нехай маємо трикутник ABC, Кут З-прямої, СК - висота до гіпотенузи
 (CK)^2=AK*KB=16*9=144 
CK=sqrt(144)=12
(CB)^2=(CK)^2+(KB)^2=144+81=225
CB=15
(AC)^2=(AK)^2+(CK)^2=256+144=400
AC=sqrt(400)=20    
S=AC*CB/2=15*20/2=150

Answer 2

Problem Analysis

We are given a right triangle with a hypotenuse and two segments divided in a ratio of 9:16. The length of the smaller leg is given as 45 cm. We need to find the area of the triangle.

Solution

To find the area of the triangle, we need to know the lengths of both legs. Let's denote the length of the smaller leg as x and the length of the larger leg as y.

According to the given information, the smaller leg is 45 cm and the ratio between the hypotenuse and the larger leg is 9:16. This means that we can write the following equation:

x/y = 9/16 We can solve this equation to find the value of y.

Solving the Equation

To solve the equation, we can cross-multiply:

16x = 9y

Now, we can isolate y by dividing both sides of the equation by 9:

y = (16x)/9

Finding the Length of the Larger Leg

We know that the length of the smaller leg (x) is 45 cm. Substituting this value into the equation, we can find the length of the larger leg (y):

y = (16 * 45)/9 = 80 cm

So, the length of the larger leg is 80 cm.

Finding the Area of the Triangle

Now that we know the lengths of both legs, we can use the formula for the area of a right triangle:

Area = (1/2) * base * height

In this case, the base is the smaller leg (x) and the height is the larger leg (y).

Substituting the values, we get:

Area = (1/2) * 45 cm * 80 cm = 1800 cm^2

Therefore, the area of the triangle is 1800 cm^2.

Conclusion

The area of the right triangle is 1800 cm^2.

Note: The search results provided by You.com did not contain the specific information needed to solve this problem. The solution was derived using the given information and the properties of right triangles.