Question

катети прямокутного трикутника відносяться,як 3:4,а його гіпотенуза дорівнює 10 см.Знайдіть катети трикутника

Answer 1

Нехай перший катет - 3х см, другий - 4х см. За т. Піфагора:
10=$\sqrt{ 3x^{2} + 4x^{2} } = \sqrt{9 x^{2} + 16x^{2} } = \sqrt{25 x^{2} } =5x$
10=5х
х=2
3х=6 (см)
4х=8 (см)
Відповідь: 6 см, 8 см 

Answer 2

Finding the Length of the Catheti of a Right Triangle

To find the lengths of the catheti of a right triangle, we can use the given information that the ratio of the catheti is 3:4 and the length of the hypotenuse is 10 cm.

Let's assume that the lengths of the catheti are 3x and 4x, where x is a common factor. According to the given ratio, we have:

Length of the first cathetus = 3x Length of the second cathetus = 4x

We know that the sum of the squares of the lengths of the catheti is equal to the square of the length of the hypotenuse, according to the Pythagorean theorem. Mathematically, this can be expressed as:

(3x)^2 + (4x)^2 = 10^2

Simplifying the equation, we get:

9x^2 + 16x^2 = 100

Combining like terms, we have:

25x^2 = 100

Dividing both sides of the equation by 25, we get:

x^2 = 4

Taking the square root of both sides, we find:

x = 2

Now that we have the value of x, we can substitute it back into the expressions for the lengths of the catheti:

Length of the first cathetus = 3x = 3 * 2 = 6 cm Length of the second cathetus = 4x = 4 * 2 = 8 cm

Therefore, the lengths of the catheti of the right triangle are 6 cm and 8 cm.

Note: The above calculations are based on the assumption that the given ratio of 3:4 refers to the lengths of the catheti. If the ratio refers to some other aspect of the triangle, please provide additional information for a more accurate answer.