Question

Ещё одна простая задача. Периметр прямоугольного треугольника равен 24 см, а один из катетов-6 см. Найди второй катет и гипотенузу. Распишите каждое решение, спасибо! )

Answer 1

Катет 6 см, гипотенуза 12 см.
24-(6+12)=6(см)
Вроде так если я не забыл геометрию...
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Answer 2

Problem Analysis

We are given a right-angled triangle with a perimeter of 24 cm and one of the legs measuring 6 cm. We need to find the length of the other leg and the hypotenuse.

Solution

Let's denote the length of the other leg as x and the length of the hypotenuse as y.

To find x, 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.

The Pythagorean theorem can be written as:

x^2 + 6^2 = y^2 (Equation 1)

We also know that the perimeter of the triangle is 24 cm. The perimeter is the sum of the lengths of all three sides of the triangle.

So, we can write the equation for the perimeter as:

x + 6 + y = 24 (Equation 2)

We have two equations (Equation 1 and Equation 2) with two unknowns (x and y). We can solve these equations simultaneously to find the values of x and y.

Solving the Equations

Let's solve the equations to find the values of x and y.

From Equation 2, we can rewrite it as:

x + y = 24 - 6 (Equation 3)

Simplifying Equation 3, we get:

x + y = 18 (Equation 4)

Now, we can substitute the value of y from Equation 4 into Equation 1:

x^2 + 6^2 = (18 - x)^2

Expanding the equation, we get:

x^2 + 36 = 324 - 36x + x^2

Simplifying the equation, we get:

36x = 288

Dividing both sides of the equation by 36, we get:

x = 8

Now, we can substitute the value of x into Equation 4 to find y:

8 + y = 18

Simplifying the equation, we get:

y = 10

Therefore, the length of the second leg (x) is 8 cm and the length of the hypotenuse (y) is 10 cm.

Answer

The length of the second leg is 8 cm and the length of the hypotenuse is 10 cm.