Question

In each of the following figures, ABCD is a parallelogram. In each case, given above, find the values of x and y. ​

Answer 1

Answer:

x=5

y=3

Step-by-step explanation:

6y+2=4x

3x-3=4y

=>-12y-9=-9x

12y+4=8x

=>x=5

y=3

Answer 2

Given:-

• ABCD is a parallelogram

To Find:-

• The sides of parallelogram

Solution:-

We know, that the parallel sides of a parallelogram are always equal.

In this parallelogram,

AD || BC

DC || AB

Hence,

The sides AD and BC will be equal and the sides AB and DC will be equal.

So,

AD = BC

3x - 3 = 4y

=> 3x - 4y = 3 .............. (i)

Also,

AB = DC

6y + 2 = 4x

=> 6y - 4x = -2 ............... (ii)

From equation (i)

= 3x - 4y = 3

=> 3x = 3 + 4y

=> x = $\sf{\dfrac{3+4y}{3}}$

Substituting the value of x in equation (ii)

= $\sf{6y - 4\bigg(\dfrac{3 + 4y}{3}\bigg) = -2}$

=> $\sf{\dfrac{18y -4(3 + 4y)}{3} = -2}$

=> $\sf{18y - 12 - 16y = -2\times 3}$

=> $\sf{2y = -6 + 12}$

=> $\sf{2y = 6}$

=> $\sf{y = \dfrac{6}{2}}$

=> $\sf{y = 3}$

Putting the value of y in equation (i)

= 3x - 4y = 3

=> 3x - 4 × 3 = 3

=> 3x - 12 = 3

=> 3x = 3 + 12

=> 3x = 15

=> x = 15/3

=> x = 5

Now,

Putting the values of x and y in respective sides:-

AB = 4x = 4 × 5 = 20 cm

BC = 3x - 3 = 3 × 5 - 3 = 15 - 3 = 12 cm

CD = 6y + 2 = 6 × 3 + 2 = 18 + 2 = 20 cm

DA = 4y = 4 × 3 = 12 cm

Here,

AB = CD and BC = DA [Hence Verified too]

_____________________________________