What must the length of segment ad be for the quadrilateral to be a parallelogram?

10 answers
Question:

What must the length of segment ad be for the quadrilateral to be a parallelogram?

[tex]What must the length of segment ad be for the quadrilateral to be a parallelogram?[/tex]


Answers

The answer is 31 units

[tex]AD=31\ units[/tex]

Step-by-step explanation:

we know that

In a Parallelogram opposite sides are equal in length and opposite angles are equal in measure

so

in this problem

To be a parallelogram

[tex]AD=BC[/tex]

[tex]AB=DC[/tex]

we have

[tex]AD=3x+7[/tex] -----> equation A

[tex]BC=5x-9[/tex] ------> equation B

equate equation A and equation B

[tex]3x+7=5x-9[/tex]

solve for x

[tex]5x-3x=7+9[/tex]

[tex]2x=16[/tex]

[tex]x=8\ units[/tex]

Find the length of segment AD

[tex]AD=3x+7[/tex]

[tex]AD=3(8)+7=31\ units[/tex]

  31 units

Step-by-step explanation:

When the figure is a parallelogram, opposite sides have the same measure:

  AD = BC

  3x +7 = 5x -9 . . . . . . substitute given expressions

  16 = 2x . . . . . . . . . . . add 9-3x

  8 = x . . . . . . . . . . . . . divide by 2

Use this value of x in the expression for AD to find its required length:

  AD = 3(8) +7 = 24 +7

  AD = 31 . . . . units

The length of segment AD must be 31 units for ABCD to be a parallelogram.

31

Step-by-step explanation:

I got it right

31 units

Step-by-step explanation:

I just did it

31

Step-by-step explanation:

AD=BC

Step-by-step explanation:

For the Quadrilateral to be parallelogram it is compulsory that the one pair of opposite sides must be parallel as well as equal, one pair is enough since that will  make the other also  to follow the same property.

So on the basis of the above statement AD must have the length equal to BC since it is given that AD is parallel to BC.

Since the length of BC can be any of the options from given units and same length AD must have.

it's 31

Step-by-step explanation:

the answer is C. 31 units

I just did the assignment

There seems to be something missing. Either a missing diagram or more context to the problem, or perhaps more instructions. I'm not exactly sure.

Anyways, if you simply need to solve the equation for x, then...
3x+7 = 5x-9
3x+7-3x = 5x-9-3x ... subtract 3x from both sides
7 = 2x-9
7+9 = 2x-9+9 ... add 9 to both sides
16 = 2x
2x = 16
2x/2 = 16/2 ... divide both sides by 2
x = 8

I'm assuming after this point, you'll use x somehow to determine the length of segment AD. Unfortunately there isn't enough info provided to do that, but I'll let you take over from here.

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