Math, asked by pratikpatole63, 1 year ago

In the figure, the sides of a rectangle are
given. The lengths are in cm. Find the length
and breadth of the rectangle.
4x + 2y
2x+y+2
3x-y+3
2x+3y + 4​

Answers

Answered by none59
11

Answer:

4x+2y = 2x+3y+4 (opposite sides of a

rectangle are equal)

Eq. 1

2x+y+2 = 3x-y+3 (opposite sides of a

rectangle are equal)

Eq. 2

Solving 1,

2x = y+4

y = 2x-4

Solving 2,

2y = x+1

Substituting the value of y from Eq. 1 to Eq. 2,

2(2x-4) = x+1

4x-8 = x+1

3x = 9

x = 3

Putting the value of x in Eq. 1,

y = 2(3)-4

y = 6-4

y = 2

x = 3 and y = 2

Step-by-step explanation:

Answered by varadad25
49

Answer:

The length and breadth of the rectangle are 16 cm & 10 cm respectively.

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

We know that,

Opposite sides of a rectangle are congruent.

∴ AB = CD

→ 2x + y + 2 = 3x - y + 3

→ 2x + y - 3x + y = 3 - 2

→ - x + 2y = 1 - - ( 1 )

Also,

BC = AD

→ 2x + 3y + 4 = 4x + 2y

→ 4 = 4x + 2y - 2x - 3y

→ 4x + 2y - 2x - 3y = 4

→ 2x - y = 4 - - ( 2 )

By multiplying equation ( 2 ) by 2, we get,

→ 2 × ( 2x - y ) = 4 × 2

→ 4x - 2y = 8 - - ( 3 )

Now, by adding equation ( 1 ) & equation ( 3 ), we get,

- x + 2y = 1 - - ( 1 )

+

4x - 2y = 8 - - ( 3 )

___________

→ 3x = 9

→ x = 9 ÷ 3

→ x = 3

By substituting x = 3 in equation ( 1 ), we get,

- x + 2y = 1 - - ( 1 )

→ - ( 3 ) + 2y = 1

→ - 3 + 2y = 1

→ 2y = 1 + 3

→ 2y = 4

→ y = 4 ÷ 2

→ y = 2

Now,

Length of rectangle ( AD ) = 4x + 2y

→ AD = 4 × 3 + 2 × 2

→ AD = 12 + 4

→ AD = 16

∴ Length of rectangle = 16 cm

Now,

Breadth of rectangle ( AB ) = 2x + y + 2

→ AB = 2 × 3 + 2 + 2

→ AB = 6 + 2 + 2

→ AB = 8 + 2

→ AB = 10

∴ Breadth of rectangle = 10 cm.

∴ The length and breadth of the rectangle are 16 cm & 10 cm respectively.

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