Question

The area of a square field is 5184 m² . A rectangular field , whose length is twice its breadth, has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field.​

Answer 1

For square field:

• Area of square field = 5184 m²

Area = (side)²

→ 5184 = (side)²

→ Side = √5184

→ Side = 72 m

For rectangular field:

• Length = 2 × Breadth

Let

• Length be l
• Breadth be b

Perimeter of rectangular field = Perimeter of square field

➝ 2 (l + b) = 4 × side

➝ 2 (2b + b) = 4 × side

➝ 2 (3b) = 4 × 72

➝ 6b = 288

➝ b = 288 ÷ 6

➝ b = 48 m

For finding the length,

Length = 2 × Breadth

⇒ Length = 2 × 48

⇒ Length = 96 m

Now we know length and breadth. So, let's find the area of the rectangular field.

Area of rectangular field = Length × Breadth

⇒ Area of rectangular field = 96 × 48

∴ Area of rectangular field = 4608 m²

Answer 2

${\large{\underline{\underline{\textsf{\textbf{Given\:: -}}}}}}$

↝ Area of square field

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\textsf{\textbf{To Find\:: -}}}}}}$

↝ Area of Rectangle

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\textsf{\textbf{Using Formulae\:: -}}}}}}$

$\small{\bigstar{\underline{\boxed{\bf{\pink{Side \: of \: square = \sqrt{Area \: of \: square}}}}}}}$

$\small{\bigstar{\underline{\boxed{\bf{\pink{Perimeter \: of \: square = 4a}}}}}}$

$\small{\bigstar{\underline{\boxed{\bf{\pink{Perimeter \: of \: rectangle = 2(Lenght + Breadth)}}}}}}$

$\small{\bigstar{\underline{\boxed{\bf{\pink{Area \: of \: Rectangle = Length \times Breadth}}}}}}$

$\begin{gathered}\end{gathered}$

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

$\red\bigstar$ Fistly, Finding the side of square :-

${\dashrightarrow{\sf{Side_{(Square)} = \sqrt{Area \: of \: square}}}}$

Substuting the value

${\dashrightarrow{\sf{Side_{(Square)} = \sqrt{5184 \: {m}^{2} }}}}$

${\dashrightarrow{\sf{Side_{(Square)} = \sqrt{72 \times 72}}}}$

${\dashrightarrow{\sf{Side_{(Square)} = {72 \: m}}}}$

${\bigstar{\purple{\underline{\boxed{\bf{Side \: of \: square = {72 \: m}}}}}}}$

∴ The side of square is 72 m.

$\begin{gathered}\end{gathered}$

$\red\bigstar$ Now, Finding the perimeter of square :-

${\dashrightarrow{\sf{Perimeter_{(Square)} = 4a}}}$

Substuting the values

${\dashrightarrow{\sf{Perimeter_{(Square)} = 4(72)}}}$

${\dashrightarrow{\sf{Perimeter_{(Square)} = 4\times 72}}}$

${\dashrightarrow{\sf{Perimeter_{(Square)} = 288 \: m}}}$

${\bigstar{\underline{\boxed{\bf{\purple{Perimeter \: of \: square = 288 \: m}}}}}}$

∴ The perimeter of square is 288 m.

$\begin{gathered}\end{gathered}$

$\red\bigstar$ Here :-

↝ Perimeter of Square = Perimeter of Rectangle

Let the,

↝ Breadth of Rectangle = x

↝ Lenght of Rectangle = twice of breath (2×x) = 2x

$\begin{gathered}\end{gathered}$

$\red\bigstar$ Now, Finding the sides of rectangle :-

$\small{\dashrightarrow{\sf{Perimeter_{(Rectangle)} = 2(Lenght + Breadth)}}}$

Substuting the values

${\dashrightarrow{\sf{288 \: m = 2(2x + x)}}}$

${\dashrightarrow{\sf{288 \: m = 2(3x)}}}$

${\dashrightarrow{\sf{\dfrac{288}{2} = 3x}}}$

${\dashrightarrow{\sf{\cancel{\dfrac{288}{2}} = 3x}}}$

${\dashrightarrow{\sf{144 = 3x}}}$

${\dashrightarrow{\sf{x = \dfrac{144}{3} }}}$

${\dashrightarrow{\sf{x = \cancel{\dfrac{144}{3}}}}}$

${\dashrightarrow{\sf{x = 48 \: m }}}$

${\bigstar{\underline{\boxed{\bf{\purple{x = 48 \: m }}}}}}$

∴ The value of x is 48 m.

$\begin{gathered}\end{gathered}$

$\red\bigstar$ Thus :-

Breadth of Rectangle = 48 m

Lenght of Rectangle = 48×2 = 96 m

$\begin{gathered}\end{gathered}$

$\red\bigstar$ Now, Finding the area of rectangle :-

${\dashrightarrow{\sf{Area_{(Rectangle)} = Lenght \times Breadth}}}$

Substuting the values

${\dashrightarrow{\sf{Area_{(Rectangle)} = 96 \: m\times 48 \: m}}}$

${\dashrightarrow{\sf{Area_{(Rectangle)} = 4608 \: {m}^{2} }}}$

${\bigstar{\underline{\boxed{\bf{\purple{Area \: of \: rectangle = 4608 \: {m}^{2} }}}}}}$

∴ The area of rectangular field is 4608 m².

$\begin{gathered}\end{gathered}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬