Question

Периметр параллелограмма АВСД равен 37см. Если периметр треугольника ВСД равен 25.4 см, то длина диагонали ВД равна?

Answer 1

BC+CD=37/2
Pbcd=BC+CD+BD
BD=25,4-18,5=6,9

Answer 2

37:2=18,5 это вс и сд, в параллелограмме противоположные стороны равны

а периметр это вс+сд+вд    25,4-18,5=6,9 это вд

Answer 3

Perimeter of Parallelogram ABCD

To find the length of diagonal BD in parallelogram ABCD, we need to use the given information about the perimeter of the parallelogram and the perimeter of triangle VSD.

Let's denote the length of side AB as a, the length of side BC as b, the length of side CD as c, and the length of side DA as d.

The perimeter of parallelogram ABCD is given as 37 cm. This means that the sum of all four sides of the parallelogram is 37 cm.

The perimeter of triangle VSD is given as 25.4 cm. This means that the sum of the three sides of the triangle is 25.4 cm.

Using these two pieces of information, we can set up the following equations:

Equation 1: a + b + c + d = 37 cm (perimeter of parallelogram ABCD) Equation 2: b + c + d = 25.4 cm (perimeter of triangle VSD)

To find the length of diagonal BD, we need to find the value of side a.

Subtracting Equation 2 from Equation 1, we get:

(a + b + c + d) - (b + c + d) = 37 cm - 25.4 cm a = 11.6 cm

Therefore, the length of side AB is 11.6 cm.

Now, we can use the properties of a parallelogram to find the length of diagonal BD.

In a parallelogram, the diagonals bisect each other. This means that diagonal BD divides the parallelogram into two congruent triangles.

Since triangle VSD is congruent to the triangle formed by diagonal BD and the two adjacent sides of the parallelogram, we can use the perimeter of triangle VSD to find the length of diagonal BD.

The perimeter of triangle VSD is given as 25.4 cm, and we know that the sum of the lengths of the two sides adjacent to diagonal BD is 11.6 cm.

Therefore, the length of diagonal BD is half the perimeter of triangle VSD minus the sum of the lengths of the two adjacent sides:

Length of diagonal BD = (25.4 cm - 11.6 cm) / 2 = 6.9 cm

So, the length of diagonal BD in parallelogram ABCD is 6.9 cm.