Question

!!Срочно!! Сума катетів прямокутного трикутника дорівнює 14 см, а його гіпотенуза 10 см. Знайдіть периметр трикутника.​

Answer 1

За теоремою Піфагора в прямокутному трикутнику квадрат гіпотенузи дорівнює сумі квадратів катетів, тому:

гіпотенуза^2 = катет1^2 + катет2^2

10^2 = катет1^2 + катет2^2

100 = катет1^2 + катет2^2

14 = катет1 + катет2

Answer 2

Calculation of the Perimeter of a Right Triangle

To find the perimeter of a right triangle, we need to know the lengths of all three sides. In this case, we are given the lengths of the two legs (or catheti) and the hypotenuse of the triangle.

Given: - Length of one leg (cathetus): 14 cm - Length of the hypotenuse: 10 cm

To find the length of the other leg, 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 two legs.

Using the Pythagorean theorem, we can calculate the length of the other leg as follows:

a^2 + b^2 = c^2

Where: - a and b are the lengths of the legs - c is the length of the hypotenuse

In this case, we have: - a = 14 cm - c = 10 cm

Substituting these values into the equation, we get:

14^2 + b^2 = 10^2

Simplifying the equation, we have:

196 + b^2 = 100

Subtracting 196 from both sides, we get:

b^2 = 100 - 196

Simplifying further, we have:

b^2 = -96

Since the length of a side cannot be negative, we can conclude that there is no real solution for the length of the other leg. Therefore, the given lengths do not form a valid right triangle.

As a result, we cannot calculate the perimeter of the triangle with the given information.

Please let me know if there's anything else I can help you with!