Question

MNKP – параллелограмм. Найдите длину диагонали МК, если периметр параллелограмма равен 62 см, а периметр треугольника MNK равен 44 см

Answer 1

 Р(MNKP)=2* (а+b) = 62,  a+b= 31
P(MNK)= a+b+MK=44,  MK=44-31=13

Answer 2

Finding the Length of Diagonal MK in a Parallelogram

To find the length of diagonal MK in a parallelogram, we need to use the given information about the perimeter of the parallelogram and the perimeter of triangle MNK.

Let's denote the length of diagonal MK as x.

Perimeter of the Parallelogram

The perimeter of a parallelogram is equal to the sum of the lengths of all its sides. In this case, the perimeter of the parallelogram is given as 62 cm.

Perimeter of Triangle MNK

The perimeter of a triangle is equal to the sum of the lengths of all its sides. In this case, the perimeter of triangle MNK is given as 44 cm.

Relationship between the Perimeter of the Parallelogram and the Perimeter of Triangle MNK

In a parallelogram, the sum of the lengths of the adjacent sides is equal to the sum of the lengths of the diagonals. Therefore, we can write the following equation:

2(MK + MN) = 62 cm

In triangle MNK, the sum of the lengths of the sides is equal to the perimeter of the triangle. Therefore, we can write the following equation:

MN + NK + MK = 44 cm

Solving the Equations

We have two equations with two unknowns (MK and MN). We can solve these equations simultaneously to find the length of diagonal MK.

From the equation 2(MK + MN) = 62 cm, we can simplify it to:

MK + MN = 31 cm

Substituting this value into the equation MN + NK + MK = 44 cm, we get:

31 cm + NK = 44 cm

Simplifying further, we find:

NK = 44 cm - 31 cm NK = 13 cm

Now, we can substitute the value of NK into the equation MK + MN = 31 cm:

MK + 13 cm = 31 cm

Simplifying further, we find:

MK = 31 cm - 13 cm MK = 18 cm

Therefore, the length of diagonal MK in the parallelogram is 18 cm.