Question

Площадь равнобокой трапеции mnkp с основаниями mn и kp равно 40м^2. высота mh=5( или 6) корней из 2 м, а длина стороны kp на 2 корня из 2 м больше, чем длина стороны mn. каковы длины сторон трапеции?

Answer 1

Ответ: Точно не знаю правильно или нет

Answer 2

To find the lengths of the sides of the trapezoid MNKP, we can use the given information about its area, height, and the relationship between the lengths of its sides.

Let's break down the information provided:

- The area of the trapezoid MNKP is 40 m^2. - The height MH is either 5 or 6 square roots of 2 meters. - The length of side KP is 2 square roots of 2 meters longer than the length of side MN.

Finding the lengths of the sides:

Let's assume the length of side MN is x meters. Since the length of side KP is 2 square roots of 2 meters longer than the length of side MN, the length of side KP can be expressed as (x + 2√2) meters.

The formula for the area of a trapezoid is given by:

Area = (1/2) * (sum of the lengths of the bases) * height

Substituting the given values into the formula, we have:

40 = (1/2) * (MN + KP) * MH

Since we know that MH is either 5 or 6 square roots of 2 meters, we can substitute these values one by one and solve for the lengths of the sides.

Case 1: MH = 5√2

Substituting MH = 5√2 into the equation, we have:

40 = (1/2) * (MN + KP) * (5√2)

Simplifying the equation, we get:

80 = (MN + KP) * (5√2)

Dividing both sides of the equation by 5√2, we have:

16 = MN + KP

Since we know that KP = MN + 2√2, we can substitute this value into the equation:

16 = MN + (MN + 2√2)

Simplifying the equation, we get:

16 = 2MN + 2√2

Dividing both sides of the equation by 2, we have:

8 = MN + √2

Subtracting √2 from both sides of the equation, we get:

8 - √2 = MN

Therefore, the length of side MN is 8 - √2 meters.

Since KP = MN + 2√2, we can substitute the value of MN into this equation:

KP = (8 - √2) + 2√2

Simplifying the equation, we