Question

the area of a square field is 5184 m square a rectangular field whose length is twice its breadth has its perimeter is equal to the perimeter of a square field find the area of the rectangular field​

Answer 1

$\huge\underline\frak\blue{Given}$

• Area of Square = 5184m^2

• Length of Rectangle (l) = 2×breadth(b)

• Perimeter of Square = Perimeter of Rectangle

$\huge\underline\frak\blue{To\:find}$

• Area of Rectangle

$\huge\underline\frak\blue{Solution}$

We have,

Area of Square

$= > {a}^{2} = 518 4 \\ = > a = \sqrt{5184} = 72m$

Hence,

• Side a of square = 72cm

• Perimeter of Square = 4a

$= > 4 \times 72 = 288m$

Perimeter of Square = 288m

Now,

• Perimeter of Square = Perimeter of Rectangle

So,

• Perimeter of Rectangle = 2(l + b)

And,

We have, length(l) = 2b, breadth = b

So,

$= > 2(2b + b) = 288 \\ = > (2b + b) = \frac{288}{2} = 144 \\ = > 3b = 144 \\ = > b = \frac{144}{3} = 48m$

Then,

• Length = 2b = 2× 48 = 96m

• Breadth = b = 48m

Area of Rectangle = l × b

So,

Area of Rectangle = 96 × 48 = 4608m^2

Answer 2

Solution :

Given area of square field = $\sf \: 5184 {m}^{2}$

We know that,

$\bigstar \boxed{ \sf \: Area \: of \: square = ({Side})^{2} }$

$\sf \longrightarrow \: 5184 = ({Side})^{2}$

$\sf \longrightarrow \: {Side \: } = \sqrt{5184}$

$\sf \longrightarrow \: {Side \: } = \sqrt{72 \times 72}$

$\sf \longrightarrow \red{ {Side \: } = 72 \: m }$

Now,Move to the rectangular portion :

Given length of the rectangular field is twice its breadth.

Let breadth of field be x and length be 2x

Also given the Perimeter of Rectangular field is equal to the Perimeter of Square Field

$\bigstar \boxed{ \sf Perimeter \: of \: Rectangle= 2(length + breadth)}$

$\bigstar \boxed{ \sf Perimeter \: of \: Square = 4 \times side}$

According to the Question :

$\longrightarrow \sf \: 2(l + b) = 4 \times side$

$\longrightarrow \sf \: 2(2x+ x) = 4 \times 72$

$\longrightarrow \sf \:4x + 2x= 288$

$\longrightarrow \sf \:6x= 288$

$\longrightarrow \sf \:x = \cancel\dfrac{288}{6}$

$\sf \longrightarrow \red{ {x \: } = 48 }$

Therefore,Length of the rectangle = 48 m

And Breadth = 2(48) = 96 m

Now, Let's Find Area of the Rectangular Field :

$\bigstar \boxed{ \sf \: Area \: of \: rectangle = Length \times Breadth}$

$\longrightarrow \sf \: 48 \times 96$

$\longrightarrow \sf \large \boxed{ \purple{ \sf \: 4608{m}^{2} }}$

Hence, Area of the Rectangular Field is 4608 m^2 .