Question

Диагональ квадрата 10 см .найдите периметр квадрата

Answer 1

Т.к. диагональ в квадрате эт гипотенуза прямоугольного треугольника, то a^2+b^2=100. А т.к. диагональ квадрата делит угол на равные части, то треугольник равнобедренный(углы при диагонали равны), следовательно a=b=√50=5√2 (см). P=4a=4*5√2=20√2 (см)

Answer 2

To find the perimeter of a square, you need to know the length of one side of the square. Since the diagonal of the square is given as 10 cm, we can use the Pythagorean theorem to find the length of one side.

Let's assume the length of one side of the square is "s" cm.

According to the Pythagorean theorem, in a square, the diagonal (d) is the hypotenuse of a right-angled triangle with the sides of length "s" (one side of the square) and "s" (another side of the square). The formula for the diagonal of a square in terms of the side length (s) is:

d = √(s^2 + s^2) d = √(2s^2) d = s√2

Given that the diagonal (d) is 10 cm, we can now solve for "s":

10 = s√2 s = 10 / √2 s = 10 / 1.4142 (approximating √2 to 4 decimal places) s ≈ 7.071 cm

Now that we have the side length (s), we can find the perimeter (P) of the square:

P = 4s P = 4 * 7.071 P ≈ 28.284 cm

So, the perimeter of the square is approximately 28.284 cm.