contestada

The perimeter of parallelogram ABCD is equal to 10 cm. Find the length of diagonal BD if you know that the perimeter of △ABD is 8 cm.

Respuesta :

calculista
see the attached figure

Let
P1-------------> Perimeter of parallelogram ABCD
P2-------------> Perimeter of △ABD

we know that
P1=10 cm
P1=2*(AD)+2*(AB)=10------------> AB+AD=5-----------> equation 1
and
P2=AD+AB+DB
P2=8 cm------------>AD+AB+DB=8-------- AB+AD=8-DB-----> equation 2
I substitute 1 in 2

(5)=8-DB----------> DB=8-5-----------> DB=3 cm

the answer is DB=3 cm

Ver imagen calculista
xero099

The length of the diagonal BD is 3 centimeters.

Procedure - Length determination in a parallelogram side

A parallelogram is a quadrilateral where each pair of parallel sides have the same length and can be form by two congruent triangles which share the same side (diagonal).

Expressions for the parallelogram

Perimeter equations for the parallelogram are the following:

[tex]AB + BD + AD = 8\,cm[/tex] (1)

[tex]2\cdot AB + 2\cdot AD = 10\,cm[/tex] (2)

Where:

  • [tex]AB[/tex], [tex]AD[/tex] - Side lengths of the parallelogram, in centimeters.
  • [tex]BD[/tex] - Diagonal length of the parallelogram, in centimeters.

Resolution of the system

By (2) we have the following conclusion:

[tex]AB + AD = 5\,cm[/tex]

And we find the length of the diagonal BD by (1):

[tex]5\,cm + BD = 8\,cm[/tex]

[tex]BD = 3\,cm[/tex]

The length of the diagonal BD is 3 centimeters. [tex]\blacksquare[/tex]

To learn more on parallelograms, we kindly invite to check this verified question: https://brainly.com/question/1563728

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