Question

2. У рівнобедрений прямокутний трикутник, катет якого дорівнює 7 см, вписано квадрат так, що вони мають спільний кут. Знайди периметр квадрата.​ ДАЮ 30 БАЛЛОВ

Answer 1

Ответ: тримай ^^

Объяснение:

Answer 2

Problem Analysis

We are given a right-angled triangle with one of its legs measuring 7 cm. The triangle is inscribed in a square, and they share a common angle. We need to find the perimeter of the square.

Solution

To find the perimeter of the square, we need to determine the length of one side of the square. Since the triangle is inscribed in the square, the hypotenuse of the triangle is equal to the diagonal of the square.

Let's use the Pythagorean theorem to find the length of the hypotenuse of the triangle.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

In this case, one of the legs of the triangle is given as 7 cm. Let's assume the other leg is x cm.

According to the Pythagorean theorem, we have:

c^2 = a^2 + b^2

Substituting the given values, we get:

c^2 = 7^2 + x^2

Simplifying the equation, we have:

c^2 = 49 + x^2

Now, let's find the value of x by solving the equation.

Taking the square root of both sides, we get:

c = sqrt(49 + x^2)

Since c is the diagonal of the square, it is equal to the side length of the square.

Therefore, the perimeter of the square is given by:

Perimeter = 4 * side length

Substituting the value of the side length, we have:

Perimeter = 4 * sqrt(49 + x^2)

To find the perimeter of the square, we need to determine the value of x.

Calculation

Let's solve the equation to find the value of x.

c = sqrt(49 + x^2)

Since the triangle is right-angled, we can use the Pythagorean theorem to find the value of x.

7^2 + x^2 = c^2

Substituting the value of c, we have:

7^2 + x^2 = (sqrt(49 + x^2))^2

Simplifying the equation, we get:

49 + x^2 = 49 + x^2

This equation is true for all values of x. Therefore, we can conclude that the value of x can be any real number.

Since the value of x can be any real number, the perimeter of the square can also be any real number.

Therefore, the perimeter of the square is not uniquely determined by the given information.

Conclusion

The perimeter of the square cannot be determined with the given information. The value of x can be any real number, which means the perimeter of the square can also be any real number.

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