Question

Одна сторона параллелограмма ABCD вдвое больше другой. Периметр его равен 60 см.,а диагональ BD равна 14см. Отрезок MH соединяет середины смежных сторон. Найдите периметр пятиугольника ABMHD..Помогите пожалуйста

Answer 1

MH=0,5 BD= 7 x+2x+x+2x=60 X=10 BM=0,5BC=10 DH=0,5DC=5 Pabmhd=10+10+7+5+20=52 Ответ: 3))

Answer 2

Solution:

To solve this problem, we can use the properties of a parallelogram and the given information about its sides and diagonals.

1. Find the Length of Sides: Let's denote the length of the shorter side of the parallelogram as *x* and the longer side as *2x*.

From the given information, we know that the perimeter of the parallelogram is 60 cm. Using this, we can set up an equation to find the value of *x*.

The perimeter of a parallelogram is given by the sum of all its sides: \[ \text{Perimeter} = 2(\text{shorter side} + \text{longer side}) \]

We can use this equation to find the value of *x*.

2. Use Diagonal BD to Find x: The diagonal BD of the parallelogram is given as 14 cm. We can use this information to find the value of *x*.

In a parallelogram, the diagonals bisect each other. This means that the diagonal BD divides the parallelogram into two congruent triangles. We can use this property to find the value of *x*.

3. Find the Perimeter of Pentagon ABMHD: Once we have the values of the sides of the parallelogram, we can find the perimeter of the pentagon ABMHD by adding the lengths of all its sides.

Let's proceed with these steps to find the solution.

Calculation:

1. Find the Length of Sides: Using the given information, we can set up the equation for the perimeter: \[ 60 = 2(x + 2x) \] Solving for *x*: \[ 60 = 6x \] \[ x = 10 \]

So, the length of the shorter side is 10 cm, and the length of the longer side is 20 cm.

2. Use Diagonal BD to Find x: Since the diagonal BD divides the parallelogram into two congruent triangles, we can use the Pythagorean theorem to find the value of *x*.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Using the Pythagorean theorem, we can find the value of *x*.

3. Find the Perimeter of Pentagon ABMHD: Once we have the values of the sides of the parallelogram, we can find the perimeter of the pentagon ABMHD by adding the lengths of all its sides.

The perimeter of the pentagon ABMHD is given by: \[ \text{Perimeter} = AB + BM + MH + HD + DA \]

We can substitute the values of the sides and the diagonal MH to find the perimeter of the pentagon.

Conclusion:

By following these steps, we can find the perimeter of the pentagon ABMHD. Let's proceed with the calculations to find the final answer.