Question

Найдите сторону ромба,если его площадь равна 8 корней из 2см в квадрате,а угол равен 45

Answer 1

Дано:

ABCD ромб

AB = 8√2 кв.см

α=45°

 

S = AB² * sinα =>

AB = √(S/sinα) = √[(8√2) / (√2/2)]  = √4 = 2 см

 

Ответ: 2 см

 

Answer 2

Finding the Side Length of a Rhombus

To find the side length of a rhombus when its area is given as 8√2 cm² and the angle is 45 degrees, we can use the formula for the area of a rhombus and the properties of a rhombus.

The formula for the area of a rhombus is: Area = (diagonal1 * diagonal2) / 2

Given that the angle is 45 degrees, we can use the properties of a rhombus to find the relationship between the side length and the diagonals.

The relationship between the side length and the diagonals of a rhombus is: Area = (diagonal1 * diagonal2) / 2 = (side length)² * sin(θ)

Where: - θ is the angle between the diagonals - side length is the length of one side of the rhombus

Using this relationship, we can solve for the side length of the rhombus.

Calculating the Side Length

Given: - Area = 8√2 cm² - Angle = 45 degrees

We can use the formula to calculate the side length: Area = (side length)² * sin(θ)

Plugging in the given values: 8√2 = (side length)² * sin(45°)

Using the fact that sin(45°) = √2 / 2: 8√2 = (side length)² * (√2 / 2)

Solving for the side length: (side length)² = (8√2) / (√2 / 2) (side length)² = 8 * 2 side length = √16 side length = 4 cm

So, the side length of the rhombus is 4 cm.