Question

Один катет прямоугольного треугольника в два раза больше другого гипотенуза равна 10 найти больший катт

Answer 1

Первый катет - х
второй катет - 2х

по теореме Пифагора, сумма квадратов катетов равна квадрату гипотенузы

х²+2х²=10²
3х²=100
х=√100/3 = 10/√3 - первый катет

2* 10√3=20√3 - второй катет

Answer 2

Finding the Length of the Hypotenuse and the Catheti

To find the lengths of the catheti and the hypotenuse of a right-angled triangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the lengths of the catheti as x and 2x and the length of the hypotenuse as c.

According to the given information, we have the following equation: x^2 + (2x)^2 = c^2

Solving for the Hypotenuse

By substituting the given values, we get: x^2 + 4x^2 = c^2 5x^2 = c^2 c = √(5x^2)

Finding the Value of x

We are also given that the hypotenuse is equal to 10: c = 10

By substituting this value, we can solve for x: 10 = √(5x^2) 100 = 5x^2 x^2 = 20 x = √20

Calculating the Length of the Hypotenuse

Now that we have the value of x, we can calculate the length of the hypotenuse: c = √(5 * 20) c = √100 c = 10

Conclusion

Therefore, the length of the hypotenuse is 10 and the lengths of the catheti are √20 and 2√20.