Find the lenghth of AB sides of ABCD parallelogram AD = (3/5)AB . Perimeter of ABCD is 11.2 cm .

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

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The perimeter of the parallelogram ABCD is:

AB+BC+CD+AD = 11.2

But we know that AB=CD and BC=AD

==> 2AB +2AD = 11.2

We also have AD=(3/5) AB

==>  2AB+ 2(3/5)AB=11.2

==> (16/5) AB = 11.2

==> AB = (11.2) (5/16) = 3.5

Then AD = (3/5) *3.5 = 2.1

pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

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We know that the perimeter of this figure must be equal to the sum of 2 times each side.  So

2AD + 2 AB = 11.2

We know that AD is 3/5 of AB and 3/5 = .6.  So

AD = .6 AB

Now we substitute -- we put in .6 AB in the place of AD.

2 (.6 AB) + 2 AB = 11.2

1.2 AB + 2 AB = 11.2

3.2 AB = 11.2

AB = 3.5

So the length of the side AB is 3.5.

If AB = 3.5 and AD = .6(3.5) then

AD = 2.1

lit24's profile pic

lit24 | College Teacher | (Level 3) Valedictorian

Posted on

ABCD is a parallelogram therefore  it's opposite sides are equal and parallel.

AB=CD and AD=BC

It is stated that,

AD=(3/5)AB

So the perimeter of the parallelogram = the sum of all the four sides:

P=2AB+2AD=2(AB+AD)=2[AB+(3/5)AB]

By substituting the values we get,

11.2 = 2[AB+(3/5)AB]

5.6 = AB+(3/5)AB

By multiplying the denominator on both sides of the equation we get,

5 x 5.6 = 5 x AB + 3 x AB

28 = 8AB

AB=7/2cm

AB=3.5cm

AD= (3/5)AB

AD= (3/5)*3.5

AD=2.1cm

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

If ABCD is a parallelogram, it's opposite sides are equal and parallel.

AB=CD and AD=BC

From the enunciation we'll have:

AD=(3/5)AB

We'll calclualte the perimeter of the parallelogram:

P=2AB+2AD=2(AB+AD)=2[AB+(3/5)AB]

We'll substitute in the formula of perimeter all we know:

11.2 = 2[AB+(3/5)AB]

5.6 = AB+(3/5)AB

We notice that we'll have to have the same denominator, both sides of equality, the denominator being 5.

5*5.6 = 5*AB + 3*AB

28 = 8AB

AB=7/2cm

AB=3.5cm

AD= (3/5)AB

AD= (3/5)*3.5

AD=2.1cm

rnk's profile pic

rnk | Student, Grade 10 | (Level 1) Honors

Posted on

We know opposite sides of a llgm are equal,

therefore,

AB = CD

AD = BC

AB+CD+AD+BC = 11.2

AB+AB+(3AB/5)+(3AB/5)=11.2

16AB/5 = 11.2

16AB = 11.2*5 = 56

AB = 56/16 = 3.5cm

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

In a parallelogram, opposite sides are equal. So Therefore

The perimeter = 2 (AD+AB) = 2{(3/5)AB +AB} = 16/5 AB which is given to be 11.2cm .Or

(16/5) AB = 11.2 cm. Or

AB = (11.2)5/16 = 56/16 = 3.5 cm.

AD = (3/5)AB = (3/5)(3.5) = 2.1 cm

iesha9182's profile pic

iesha9182 | Student, Grade 9 | eNotes Newbie

Posted on

If ABCD is a parallelogram, it's opposite sides are equal and parallel.

AB=CD and AD=BC

AD=(3/5)AB

calclualte the perimeter of the parallelogram:

P=2AB+2AD=2(AB+AD)=2[AB+(3/5)AB]

We'll substitute in the formula of perimeter :

11.2 = 2[AB+(3/5)AB]

5.6 = AB+(3/5)AB

We notice that we'll have to have the same denominator, both sides of equality, the denominator being 5.

5*5.6 = 5*AB + 3*AB

28 = 8AB

AB=7/2cm

AB=3.5cm

AD= (3/5)AB

AD= (3/5)*3.5

AD=2.1cm

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