Question

Одна із сторін прямокутника 12 см, а його діагональ 37 см. Обчислити периметр прямокутника

Answer 1

Объяснение:

Длина а=12 см

Диагональ с=37 см

Найти : Р

Решение :

По теореме Пифагора :

С^2=а^2+b^2

b^2=c^2-a^2=37^2-12^2=1369-144=

=1225

b=корень 1225=35 см

Р=2(а+b)=2(12+35)=94 см

Ответ : Р=94 см

Answer 2

Problem Analysis

We are given the length of one side of a rectangle, which is 12 cm, and the length of its diagonal, which is 37 cm. We need to calculate the perimeter of the rectangle.

Solution

To find the perimeter of a rectangle, we need to know the lengths of both its sides. However, we only have the length of one side and the length of the diagonal.

To solve this problem, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In our case, the diagonal of the rectangle is the hypotenuse of a right-angled triangle, and the sides of the rectangle are the other two sides of the triangle. Let's denote the length of the other side of the rectangle as 'x'.

According to the Pythagorean theorem, we have the following equation:

x^2 + 12^2 = 37^2

We can solve this equation to find the value of 'x', which will give us the length of the other side of the rectangle. Once we have the lengths of both sides, we can calculate the perimeter of the rectangle.

Calculation

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

x^2 + 12^2 = 37^2

x^2 + 144 = 1369

x^2 = 1369 - 144

x^2 = 1225

Taking the square root of both sides, we get:

x = sqrt(1225)

x = 35

Now that we have the lengths of both sides of the rectangle, we can calculate the perimeter:

Perimeter = 2 * (Length + Width)

Perimeter = 2 * (12 + 35)

Perimeter = 2 * 47

Perimeter = 94 cm

Answer

The perimeter of the rectangle is 94 cm.

Explanation

We used the Pythagorean theorem to find the length of the other side of the rectangle. By substituting the values into the equation, we found that the length of the other side is 35 cm. Then, we calculated the perimeter of the rectangle by adding the lengths of both sides and multiplying by 2. The final result is a perimeter of 94 cm.