Question

Периметр квадрата равен 21,6м. Найдите его диагональ AC

Answer 1

Все стороны равны. Р=4*а, а=21,6/4=5,4 сторона квадрата
треугольник АВС прямоугольный, следовательно квадрат гипотенузы равен сумме квадратов катетов
АС^2=АВ^2+ВС^2=29,16+29,16=58,32
АС=√58,32

Answer 2

Perimeter of a Square

To find the diagonal of a square, we first need to determine the length of its sides. In this case, we are given that the perimeter of the square is 21.6 meters.

The perimeter of a square is calculated by adding up the lengths of all four sides. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of each side.

Let's calculate the length of each side:

Perimeter of the square = 21.6 meters

Length of each side = Perimeter / 4 = 21.6 / 4 = 5.4 meters

Now that we know the length of each side, we can find the length of the diagonal.

Finding the Diagonal of a Square

In a square, the diagonal forms a right triangle with two sides of equal length. The diagonal acts as the hypotenuse of this right triangle, while the sides of the square act as the two legs.

To find the length of the diagonal, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

Let's denote the length of each side of the square as a and the length of the diagonal as AC.

According to the Pythagorean theorem:

AC^2 = a^2 + a^2

Simplifying the equation:

AC^2 = 2a^2

Taking the square root of both sides:

AC = √(2a^2)

Substituting the value of a:

AC = √(2 * 5.4^2)

Calculating the value:

AC ≈ 7.64 meters

Therefore, the length of the diagonal AC is approximately 7.64 meters.