Question

В параллелограмме MNKP MN=8см, MP=7*корень из 3 см, M=30 град.Найдите диагонали параллелограмма

Answer 1

По теореме косинусов меньшая диагональ:
a^2=8^2+(7*sqrt(3))^2-2*8*7*sqrt(3)*cos(30)
a^2=64+147-168
a=sqrt(43) см
Большая диагональ:
b^2=8^2+(7*sqrt(3))^2-2*8*7*sqrt(3)*cos(150)
b^2=64+147+168
b=sqrt(379) см

Answer 2

Given Information

We are given the following information about the parallelogram MNKP: - MN = 8 cm - MP = 7√3 cm - ∠M = 30 degrees

Finding the Diagonals of the Parallelogram

To find the diagonals of the parallelogram, we can use the given information and the properties of a parallelogram.

In a parallelogram, the diagonals bisect each other. This means that the point where the diagonals intersect divides each diagonal into two equal parts.

Let's label the point where the diagonals intersect as O. Since the diagonals bisect each other, we can say that MO = ON and MP = OP.

Using this information, we can find the length of the diagonals.

Finding the Length of Diagonal MO

Since MO = ON, we can find the length of MO by dividing MN by 2.

MO = MN/2 = 8 cm/2 = 4 cm

Finding the Length of Diagonal MP

Since MP = OP, we can find the length of MP by using the given value.

MP = 7√3 cm

Answer

Therefore, the length of diagonal MO is 4 cm and the length of diagonal MP is 7√3 cm.

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