Question

В ромбе ABCD из вершины тупого угла D на сторону BC опущен перпендикуляр DK. Найдите AK, если AD=4 см, AC= 2√14 см решение НЕ через площадь. спасибо​

Answer 1

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Answer 2

Finding the Length of AK in Rhombus ABCD

To find the length of AK in rhombus ABCD, where a perpendicular DK is dropped from the vertex of the obtuse angle D to the side BC, we can use the properties of a rhombus.

Given: - AD = 4 cm - AC = 2√14 cm

We need to find AK.

Solution

In a rhombus, the diagonals bisect each other at right angles. This means that DK is the altitude of triangle ADC, and AK is the height of this triangle.

We can use the Pythagorean theorem to find AK. The Pythagorean theorem 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.

Let's denote AK as x. Then, using the given information, we can set up the following equation:

AD^2 = AK^2 + DK^2

We know that AD = 4 cm, and DK can be found using the formula for the area of triangle ADC:

Area of triangle ADC = (1/2) * base * height

Substituting the known values, we get:

Area of triangle ADC = (1/2) * AC * DK

Solving for DK, we get:

DK = (2 * Area of triangle ADC) / AC

Now, we can substitute the value of DK into the equation for AK:

4^2 = x^2 + ((2 * Area of triangle ADC) / AC)^2

Solving for x, we can find the length of AK.

Let's calculate the value of AK using the given information and the derived equations.