Question

диагонали параллелограмма равны 6корень из 2 и 8корень из 2.найти сумму квадратов всех его сторон...решите пожалуйста

Answer 1

Сумма квадратов диагоналей параллелограма равна суме квадратов всех его сторон

(6 х корень2) в квадрате + (8 х корень2) вквадрате = 72+128 =200

Сумма квадратов диагоналей =200

Answer 2

АВСД, АС=6V2 ВД=8V2

диагонали делят ромб на 4 равных прямоугольных треугольника. АВО, СВО, АДО, СДО

точка О - точка пересечения диагоналей, которая делит каждую из них пополам

значит АО=СО и ВО=ДО

рассмотрим треугольник АВО:

АО=1/2АС= 3V2 

ВО=1/2ВД= 4V2 

п теореме Пифагора АО^2+BO^2=AB^2= (3V2)^2+(4V2)^2=50

АВ^2+BC^2+CД^2+ДА^2=4*AB^2=4*50=200

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 3

Diagonals of a Parallelogram

To find the sum of the squares of all sides of a parallelogram, we first need to determine the lengths of its sides. Given that the diagonals of the parallelogram are equal to 6√2 and 8√2, we can use this information to find the lengths of the sides.

In a parallelogram, the diagonals bisect each other. This means that each diagonal divides the parallelogram into two congruent triangles. Let's label the diagonals as d1 and d2, and the sides of the parallelogram as a, b, c, and d.

Using the properties of parallelograms, we can determine the lengths of the sides in terms of the diagonals:

a = b = c = d = 0.5 * √(d1^2 + d2^2)

Substituting the given values of the diagonals, we have:

a = b = c = d = 0.5 * √((6√2)^2 + (8√2)^2) = 0.5 * √(72 + 128) = 0.5 * √200 = 0.5 * 10√2 = 5√2

Therefore, all sides of the parallelogram are equal to 5√2.

Sum of Squares of All Sides

To find the sum of the squares of all sides, we can simply square each side and add them together.

Let's calculate the sum:

Sum = a^2 + b^2 + c^2 + d^2 = (5√2)^2 + (5√2)^2 + (5√2)^2 + (5√2)^2 = 4 * (5√2)^2 = 4 * 25 * 2 = 200

Therefore, the sum of the squares of all sides of the parallelogram is 200.

Please let me know if you need any further assistance!