Question

Срочно!!!гипотенуза прямоугольного треугольника =25 а периметр =60. найти катети. надо составить уравнения и составить систему и решить её.

Answer 1

Х - один катет
у - другой катет
Система уравнений:
х+у+25=60 (формула периметра)
х²+у²=25² (т.Пифагора)
х=35-у
(35-у)²+у²=625
1225-70у+2у²=625
у²-35у+300=0
D=1225-1200=25=5²
у1=(35-5)/2=15   х1=35-15=20
у2=(35+5)/2=20    х2=35-20=15
Ответ; 15 и 20

Answer 2

Solving for the Length of the Legs of a Right-Angled Triangle

To solve for the lengths of the legs of a right-angled triangle when the hypotenuse and perimeter are given, we can use the following steps:

1. Set Up the Equations: - Let's denote the lengths of the legs of the right-angled triangle as *a* and *b*, and the hypotenuse as *c*. - We know that the perimeter (*P*) is the sum of all the sides of the triangle, so we have the equation: *a + b + c = P*. - We also know that in a right-angled triangle, the Pythagorean theorem holds true: *a^2 + b^2 = c^2*.

2. Substitute the Given Values: - In this case, the hypotenuse (*c*) is given as 25 and the perimeter (*P*) is given as 60. We can substitute these values into the equations.

3. Solve the System of Equations: - We can then solve the system of equations to find the lengths of the legs of the right-angled triangle.

Solution

1. Set Up the Equations: - Let's denote the lengths of the legs of the right-angled triangle as *a* and *b*, and the hypotenuse as *c*. - The perimeter (*P*) is the sum of all the sides of the triangle, so we have the equation: *a + b + c = 60*. - In a right-angled triangle, the Pythagorean theorem holds true: *a^2 + b^2 = c^2*.

2. Substitute the Given Values: - Given: *c = 25* and *P = 60*. - Substituting these values into the perimeter equation: *a + b + 25 = 60*.

3. Solve the System of Equations: - We can solve the system of equations to find the lengths of the legs of the right-angled triangle.

- Substituting *c = 25* into the Pythagorean theorem: *a^2 + b^2 = 25^2*.

- From the perimeter equation, we can express *b* in terms of *a*: *b = 60 - a - 25*.

- Substituting *b = 60 - a - 25* into the Pythagorean theorem: *a^2 + (60 - a - 25)^2 = 25^2*.

- Solving the equation will give us the value of *a*, and then we can find the value of *b* using the expression *b = 60 - a - 25*.

I will now calculate the values of *a* and *b* using the given equations and provide the solution.