Question

Диагональ квадрата равна 10√2см.Найдите периметр квадрата. Помогите))

Answer 1

Сторона квадрата х
диагональ d разбивает квадрат на 2 равных прямойгольных треугольника, в котором катеты - стороны квадрата, а гипотенуза - диагональ

по теореме пифагора 
x²+x²=d²
x=d/√2=10
Периметр = сумме всех сторон
P=4x=40

Answer 2

Perimeter of a Square with a Given Diagonal

To find the perimeter of a square with a given diagonal, we can use the relationship between the diagonal and the side length of a square.

Let's denote the side length of the square as s and the diagonal as d. We can use the Pythagorean theorem to relate these two values:

s^2 + s^2 = d^2

Since the diagonal of the square is given as 10√2 cm, we can substitute this value into the equation:

s^2 + s^2 = (10√2)^2

Simplifying the equation:

2s^2 = 200

Dividing both sides by 2:

s^2 = 100

Taking the square root of both sides:

s = 10 cm

Now that we have the side length of the square, we can calculate the perimeter by multiplying the side length by 4:

Perimeter = 4 * s = 4 * 10 cm = 40 cm

Therefore, the perimeter of the square is 40 cm.