Question

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

Answer 1

Given :

• Area of a square field is 5184 m².
• Perimeter of rectangle is equal to the perimeter of the square .
• Length of a rectangle is twice its breadth .

To Find :

• Area of Rectangular Field .

Solution :

Firstly we will find the side of square :

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Square={(Side)}^{2}}$

Putting Values :

$\longmapsto\tt{\sqrt{5184}=Side}$

$\longmapsto\tt\bf{72\:m=Side}$

Now , For Perimeter of Square :

Using Formula :

$\longmapsto\tt\boxed{Perimeter\:of\:Square=4\times{Side}}$

Putting Values :

$\longmapsto\tt{4\times{72}}$

$\longmapsto\tt\bf{288\:m}$

Now ,

As Given that Perimeter of rectangle is equal to the perimeter of the square . Also , Length of a rectangle is twice its breadth . So ,

$\longmapsto\tt{Let\:Breadth\:be=x}$

$\longmapsto\tt{Length=2x}$

For Perimeter of Rectangle :

Using Formula :

$\longmapsto\tt\boxed{Perimeter\:of\:Rectangle=2(l+b)}$

Putting Values :

$\longmapsto\tt{288=2(2x+x)}$

$\longmapsto\tt{\cancel\dfrac{288}{2}=2x+x}$

$\longmapsto\tt{144=3x}$

$\longmapsto\tt{\cancel\dfrac{144}{3}=x}$

$\longmapsto\tt\bf{48\:m=x}$

Therefore :

$\longmapsto\tt{Length=2(48)=96\:m}$

$\longmapsto\tt{Breadth=48\:m}$

For Area of Rectangle :

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Rectangle=l\times{b}}$

Putting Values :

$\longmapsto\tt{96\times{48}}$

$\longmapsto\tt\bf{4608\:{m}^{2}}$

So , The Area of Rectangular Field is 4608 m² .

Answer 2

Answer:

Given :-

• The area of a square field is 5184 m². The perimeter is equal to the perimeter of the square field and whose length is twice of its breadth.

To Find :-

• What is the area of a rectangular field.

Formula Used :-

$\clubsuit$ Area Of Square Formula :

$\longmapsto \sf\boxed{\bold{\pink{Area_{(Square)} =\: (a)^2}}}$

$\clubsuit$ Perimeter of Square Formula :

$\longmapsto \sf\boxed{\bold{\pink{Perimeter_{(Square)} =\: 4a}}}$

where,

• a = Side

$\clubsuit$ Perimeter of Rectangle Formula :

$\longmapsto \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}}$

$\clubsuit$ Area Of Rectangle Formula :

$\longmapsto \sf\boxed{\bold{\pink{Area_{(Rectangle)} =\: Length \times Breadth}}}$

Solution :-

First, we have to find the side of a square :

Given :

• Area of Square = 5184 m²

According to the question by using the formula we get,

$\implies \sf a^2 =\: 5184$

$\implies \sf a =\: \sqrt{5184}$

$\implies \sf a =\: 72$

$\implies \sf\bold{\purple{a =\: 72\: m}}$

Hence, the side of square is 72 m.

Now, we have to find the perimeter of square :

Given :

• Side = 72 m

According to the question by using the formula we get,

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

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

$\implies \sf\bold{\purple{Perimeter_{(Square)} =\: 288\: m}}$

Hence, the perimeter of square is 288 m.

Now, we have to find the perimeter of a rectangle :

Let,

• Breadth = x m
• Length = 2x m

According to the question by using the formula we get,

$\implies \sf 2(2x + x) =\: 288$

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

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

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

$\implies \sf \bold{\green{x =\: 48\: m}}$

Hence, the required length and breadth will be :

$\mapsto$ Breadth of a Rectangle :

$\to \sf x\: m$

$\to \sf\bold{\purple{48\: m}}$

And,

$\mapsto$ Length of a Rectangle :

$\to \sf 2x\: m$

$\to \sf 2(48)\: m$

$\to \sf 2 \times 48\: m$

$\to \sf\bold{\purple{96\: m}}$

Hence, the length and breadth of a rectangle is 96 m and 48 m respectively.

Now, we have to find the area of a rectangular field :

Given :

• Length = 96 m
• Breadth = 48 m

According to the question by using the formula we get,

$\longrightarrow \sf Area_{(Rectangular\: Field)} =\: 96\: m \times 48\: m$

$\longrightarrow \sf\bold{\red{Area_{(Rectangular\: Field)} =\: 4608\: m^2}}$

$\therefore$ The area of a rectangular field is 4608 m².