Question

ABCD is a parallelogram with AB =3x, AD =2x ,DC = 2y + 2 , and perimeter = 40 CM. Find the value of x and y

Answer 1

We know that :

opposite sides of a parallelogram are equal .

AB = CD

So:

3 x = 2 y + 2

==> 3 x - 2 y - 2 = 0.................(1)

Then perimeter = AB + BC + CD + AD

==> 3 x + 2 x + 2 y + 2 + BC = 40 cm

==> BC = AD

==> BC = 2 x

==> 5 x + 2 y + 2 + 2 x =40

==> 7 x + 2 y - 38 = 0.........................(2)

Adding 1 and 2 gives:

==> 7 x + 3 x - 40 = 0

==>1 0 x = 40

==> x = 40 / 10

= 4

3 x -2 y -2 = 0

==> 12 - 2 - 2 y = 0

==> -2y = -10

==> y = -10/-2

==> y=5

Answer:

x =  4

y = 5

Hope it helps you

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Answer 2

First of all, AD=BC, so BC also is 2x. 

Secondly, AB=CD, so 3x=2y+2. If you solve for 2y, 2y=3x-2 

Thirdly, Perimeter = Sum of four sides
2x+3x+2x+2y+2 = 40 

Simplify:
7x+2y+2=40 

Substitute 2y=3x+2:
7x + 3x-2+2=40
10x=40
x=4 

2y=3x-2
2y=3*4-2
2y=10
y=5