Question

• Refer the attached attachment for the question

Only mods good user answer ​

Answer 1

Solution :

$\red{We \: know \: that}$

•The opposite sides of

rectangle are of equal length .

$\blue{2x + y + 8 = 4x - y} \\ \\\orange{2x - 4x + y +y = - 8} \\ \\ \blue{ - 2x + 2y = - 8} \\ \\ \orange{ - x + y = - 4} \\ \\ \pink{(dividing \: both \: side \: by \: 2)} \: (1)$

$\purple{We \: Also \: \: know \: that} \\ \\ \green{x + 4 = 2y} \\ \\ \pink{x - 2y = - 4} \: \: (2)$

$\red{Adding} \: \: \green{equation (1)} \: \:\pink{and \: (2)}$

$\purple{ - x + y = - 4 (1)} \\ \\x - 2y = - 4(2)$

$\orange{We \: get} \\ \\ \blue{- y = - 8} \\ \\ \red{y = 8}$

${\green{Place \: y= 8 \: in \: equation (2)}}$

$\purple{x - 2(8) = - 4} \\ \\ x - 16 = - 4 \\ \\ \purple{x = - 4 + 16} \\ \\ x = 12$

$\red{Therefore}$

Length of Rectangle

• $\blue{=4x-y}$

• $\red{=4×(12)-8}$

• $\green{=48-8=40}$

The Breadth of the Rectangle

• $\blue{= 2 y = 2× 8 = 16}$

The Area of Rectangle = L × B

• $\purple{=40×16}$

• $\orange{640 \:sq-units}$

The perimeter of Rectangle

• $\purple{= 2 × (L× B)}$

• $\green{= 2 × (40× 16)}$

• 112 units

Final Answer :

• The area of Rectangle is 640 sq units

• It's perimeter is 112 units

Answer 2

$\textsf{\large{\underline{Solution}:}}$

We have to find out the value of x and y.

As we know that opposite sides of a rectangle are equal. Therefore:

$\sf\implies 2y = x + 4$

$\sf\implies x -2y+ 4=0 - (i)$

Also:

$\sf\implies 2x + y + 8 = 4x-y$

$\sf\implies 4x-2x-y-8-y=0$

$\sf\implies 2x-2y-8=0$

Dividing both sides by 2, we get:

$\sf\implies x-y-4=0 - (ii)$

Subtracting (ii) from (i), we get:

$\sf\implies -y+8=0$

$\sf\implies y=8$

Substituting the value of y in equation (i), we get:

$\sf\implies x-2\times8+4=0$

$\sf\implies x-16+4=0$

$\sf\implies x-12=0$

$\sf\implies x = 12$

Therefore:

$\sf\implies\begin{cases}\sf x = 12\\ \sf y = 8\end{cases}$

Now:

$\sf\implies Length = 4x-y$

$\sf\implies Length = 4\times12-8$

$\sf\implies Length = 48-8$

$\sf\implies Length = 40\ units.$

And:

$\sf\implies Breadth=2y$

$\sf\implies Breadth=2\times8$

$\sf\implies Breadth=16\ units.$

Now:

$\sf\implies Area = Length\times Breadth$

$\sf\implies Area = 40\times 16$

$\sf\implies Area=640\ sq\ units.$

The perimeter of the rectangle will be:

$\sf\implies Perimeter = 2\times(Length+Breadth)$

$\sf\implies Perimeter = 2\times(40+16)\ units.$

$\sf\implies Perimeter = 2\times56\ units.$

$\sf\implies Perimeter = 112\ units.$

$\textsf{\large{\underline{Final Answer}:}}$

• The values of x and y are - 12 and 8.
• The Length and Breadth of the rectangle are 40 and 16 units.
• The Area and Perimeter of the Rectangle are 640 square units and 112 units.