Question

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

Answer 1

• area of rectangle field is 4608m²

Given:-

• the area of square field is = 5184m²

step-by-step solution:-

⟶ s×s = 5184

⟶ s² = 5184

⟶ s = √5184

⟶ s = 72m

according to problem,

⟶ l = 2x

⟶ b=x

we know that,

perimeter of square = perimeter of rectangle

⟶ 4s = 2(l+b)

⟶ 4×72 = 2(2x+x)

⟶ 288 = 6x

⟶ x = 288/6

⟶ x = 48m.

from problem,

⟶ l = 2x

⟶ l = 2×48

⟶ l = 96m.

⟶ b = x

⟶ b= 48

Therefore,

⟶ length is 96m.

⟶  breadth is 48m.

area of rectangle = l × b

                            = 96 × 48

                         =4608 m²

Answer 2

Answer:

Given: The area of a square field is 5184 m². Find the area of rectangular field, whose perimeter is equal to the

perimeter of the square field and whose length is twice of its breadth.

$\Large {\underline{\gray{\frak { Answer \:\:: \:}}}}$

Given that ,

• The area of a square field is 5184 m².

$\quad \dag\quad \:\boxed {\underline {\frak Area_{(Square)} \:\: =\:\: Side^2 \:\:}}$

$\quad \dashrightarrow \sf Side^2 = 5184 \:\\\\ \quad \dashrightarrow \sf Side =\: \sqrt{5184}\\\\ \quad \dashrightarrow \sf Side \:=\: 72 \: \\\\ \quad \dashrightarrow \pmb Side \:=\: 72 \:m\: \bigstar$

• Hence , Side of Square is 72 m .

Now , Perimeter of Square :

$\quad \dag\quad \:\boxed {\underline {\frak Perimeter_{(Square)} \:\: =\:\: 4 \times Side \:\:}}$

$\quad \dashrightarrow \sf Perimeter = 4 \times 72 \:\\\\ \quad \dashrightarrow \sf Perimeter =\: 288 \\\\ \quad \dashrightarrow \pmb Perimeter \:=\: 288 \:m\: \bigstar$

Now , Given that ,

• The Perimeter of Rectangle is equal to the Perimeter of Square.

Therefore,

• Perimeter of Rectangle is 288 m

⊙ Let's Consider Breadth of Rectangle be x m

Given that , for Breadth of Rectangle,

• The Length of Rectangle is twice of Breadth .

Therefore,

• Length of Rectangle is 2x m .

As , We know that ,

$\quad \dag\quad \:\boxed {\underline {\frak Perimeter_{(Rectangle)} \:\: =\:\: 2( Length + Breadth)\:\:}}$

$\quad \dashrightarrow \sf 288 = 2 ( 2x + x ) \:\\\\\quad \dashrightarrow \sf 288 = 4x + 2x \:\\\\\quad \dashrightarrow \sf 288 = 6x \:\\\\ \quad \dashrightarrow \sf x = \dfrac{288}{6} \:\\\\\quad \dashrightarrow \sf x = \cancel {\dfrac{288}{6} } \:\\\\\quad \dashrightarrow \sf x = 48 \:\\\\ \quad \dashrightarrow \pmb x \:=\: 48 \:m\: \bigstar$

• Here x signifies Breadth of Rectangle which is 48 m

And ,

• Length of Rectangle is 2x = 2 × 48 = 96 m

$\sf \underline {\bigstar \:Hence \:the \:Length\: of \:the\: Rectangle\: is \:96. \:\bigstar}$