Question

The diagram shows a parallelogram ABCD. The lengths of its sides are AB = (3x + y) cm, BC = (2x - 1) cm, CD = (3y + 11) cm and DA = (x + y) cm. Find the values of x and y. ​

Answer 1

Anѕwєr :

x = 9

y = 8

Exρlαnαtion:-

We are asked to calculate the value of x and y . We can calculate value of x, y by using the properties of parallelogram . In this problem the property used is :- "In a parallelogram opposite sides are parallel and equal .

$\sf \boxed{ \huge{ \purple{ \sf AB = CD }}}$

$\sf \boxed{ \huge{ \purple{ \sf BC = AD}}}$

AB = 3x + y CD = 3y + 11

↠ 3x + y = 3y + 11

↠ 3x = 3y + 11 - y

↠ 3x = 2y + 11 .. (1)

BC = 2x-1 AD= x + y

↠ 2x -1 = x + y

↠ 2x - x = y+ 1

↠x = y + 1 ..(2)

Substituting (2) in (1)

↠3x = 2y + 11

↠3(y + 1 ) = 2y + 11

↠3y + 3 = 2y +11

↠3y - 2y = 11-3

$\: \boxed{ \large{ \sf \orange { y = 8}}}$

Substituting y value in (2)

↠x = y + 1

↠x = 8 + 1

$\: \boxed{ \large{ \sf \orange { x = 9}}}$

_________________

Vєrificαtion :-

By Substituting x, y values then it should satisfy the conditions.

AB= CD and BC = AD

AB = CD

↠3x + y = 3y + 11

↠3(9)+8 = 3(8)+11

↠27+8 = 24 +11

↠35 = 35

Hence , verified 1st condition. .

BC = AD

↠2x-1 = x + y

↠2(9)-1 = 9+8

↠ 18-1 = 17

↠17 = 17

Hence, verified 2nd condition..

Answer 2

Answer:

[tex]Anѕwєr :

x = 9

y = 8

Exρlαnαtion:-

We are asked to calculate the value of x and y . We can calculate value of x, y by using the properties of parallelogram . In this problem the property used is :- "In a parallelogram opposite sides are parallel and equal .

AB=CD

BC=AD

AB = 3x + y CD = 3y + 11

↠ 3x + y = 3y + 11

↠ 3x = 3y + 11 - y

↠ 3x = 2y + 11 .. (1)

BC = 2x-1 AD= x + y

↠ 2x -1 = x + y

↠ 2x - x = y+ 1

↠x = y + 1 ..(2)

Substituting (2) in (1)

↠3x = 2y + 11

↠3(y + 1 ) = 2y + 11

↠3y + 3 = 2y +11

↠3y - 2y = 11-3

{ y = 8}}}y=8

Substituting y value in (2)

↠x = y + 1

↠x = 8 + 1

{ x = 9}}}x=9

_________________

Vєrificαtion :-

By Substituting x, y values then it should satisfy the conditions.

AB= CD and BC = AD

AB = CD

↠3x + y = 3y + 11

↠3(9)+8 = 3(8)+11

↠27+8 = 24 +11

↠35 = 35

Hence , verified 1st condition. .

BC = AD

↠2x-1 = x + y

↠2(9)-1 = 9+8

↠ 18-1 = 17

↠17 = 17

Hence, verified 2nd condition...

ans hope it's helpful