Question

complete the following. (maths-1) 1st lesson. linear equations in two variables.



answer it please. ​

Answer 1

Solution :

We know that,

Opposite sides of rectangle are equal.

So,

2x + y + 8 = 4x - y

2x - 4x + y + y = -8

-2x + 2y = -8

-x + y = -4...(1)

Also,

x + 4 = 2y ( Opposite sides of rectangle )

So, x - 2y = -4..(2)

Adding (1) and (2),

-x + y = -4

+ x - 2y = -4

-----------------------------

-y = -8

Hence,
$\tt{\boxed{y = 8. }}$

Substituting the value of y in (2),

x - 2 (8) = -4

x - 16 = -4

$\tt{\boxed{x = 12. }}$


Hence,

x = 12.

y = 8.

Now,

Length = 4x - y

= 4 (12) - 8

= 40

Breadth = 2y

= 2 × 8

= 16

Therefore,

Length = 40

Breadth = 16

Now,

We have to find the area and perimeter.

Area = L × B

= 40 × 16

= 640 sq.units

Perimeter = 2 ( L + B )

= 2 ( 40 + 16 )

= 2 × 56

= 112 units.

Hence

Final answer :

$\mathfrak{Area = 640 sq. units}$

$\mathfrak{Perimeter = 112 units}$

Answer 2

$\mathfrak{\huge{Answer:}}$

Given are the sides of a rectangle, in the form of linear equations in $\textbf{two}$ variables.

Now, we know that the opposite sides of a rectangle are equal to one another.

Thus:-

2y = x + 4 ....(1)

2x + y + 8 = 4x - y .....(2)

Solve equation (1) further :-

=》 x = 2y - 4

Solve the equation (2) further :-

=》 2y + 8 = 4x - 2x

=》 x = $\sf{\frac{2y + 8}{2}}$

We can write that :-

x = x

=》 2y - 4 = $\sf{\frac{2y + 8}{2}}$

=》 4y - 8 = 2y + 8

=》 2y = 16

=》 $\boxed{\tt{y = 8}}$

x = 2y - 4

=》 x = 16 - 4

=》 $\boxed{\tt{x = 12}}$

Sides of the rectangle :-

2y = Breadth = 16 units

4x - y = Length = 40 units

Area of a rectangle = l × b

Area of the rectangle = 40 × 16

Area of the rectangle = 640 $\sf{units^{2}}$

Perimeter of a rectangle = 2 ( l + b )

Perimeter of the rectangle = 2 ( 40 + 16 )

Perimeter of the rectangle = 2 × 56

Perimeter of the rectangle = 112 units

Final Solution:-

$\mathfrak{x = 12\:units}$

$\mathfrak{y = 8\:units}$

$\mathfrak{Length = 40\:units}$

$\mathfrak{Breadth = 16\:units}$

$\mathfrak{Area = 640}$ $\sf{units^{2}}$

$\mathfrak{Perimeter = 112\:units}$