Question

висота прямокутного трикутника дорівнює 12 см і ділить гіпотенузу у відношенні 9:4​. Знайдіть катети трикутника

Answer 1

Ответ:
АВ=6√13см
ВС=4√13см

Решение:
Пусть АН будет 9х; НС будет 4х,
Пропорциональные отрезки прямоугольного треугольника
ВН²=АН*НС
12²=9х*4х
36х²=144
х²=144/36
х=√4
х=2
АН=9*2=18см
НС=4*2=8см
АС=АН+НС=18+8=26см

Пропорциональные отрезки
АВ=√(АН*АС)=√(18*26)=√(9*2*2*13)=
=3*2√13=6√13см
ВС=√(НС*АС)=√(8*26)=√(4*2*2*13)=
=4√13см

Answer 2

Ответ:

На фото решение

Объяснение:

Answer 3

Finding the Length of the Hypotenuse

To find the lengths of the legs of a right triangle, we first need to determine the length of the hypotenuse. In this case, we are given that the height of the right triangle is 12 cm and that it divides the hypotenuse in a ratio of 9:4.

Let's assume that the lengths of the legs of the right triangle are 9x and 4x, where x is a common factor. The length of the hypotenuse can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using this information, we can set up the following equation:

(9x)^2 + (4x)^2 = h^2

where h represents the length of the hypotenuse.

Solving for the Hypotenuse

To solve for the hypotenuse, we need to simplify and solve the equation. Expanding and simplifying the equation, we get:

81x^2 + 16x^2 = h^2

97x^2 = h^2

Taking the square root of both sides, we have:

sqrt(97x^2) = sqrt(h^2)

sqrt(97) * x = h

Therefore, the length of the hypotenuse is sqrt(97) * x.

Finding the Lengths of the Legs

Now that we know the length of the hypotenuse, we can find the lengths of the legs of the right triangle. We were given that the height of the triangle is 12 cm, so one of the legs is 12 cm.

Let's substitute the value of the hypotenuse into the equation:

sqrt(97) * x = 12

Solving for x, we have:

x = 12 / sqrt(97)

Therefore, one of the legs of the right triangle is 9x = 9 * (12 / sqrt(97)) and the other leg is 4x = 4 * (12 / sqrt(97)).

Final Answer

To summarize, the lengths of the legs of the right triangle are approximately:

Leg 1: 9 * (12 / sqrt(97)) cm

Leg 2: 4 * (12 / sqrt(97)) cm

Please note that the values provided are approximate due to the presence of the square root in the calculations.