Question

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

Answer 1

Given

Area of square field = 5184m

And ,perimeter of square = perimeter of rectangle

Let,

Breadth of retangular field = x

Length of rectangular field =2x

We know

side × side = area of square field

S^2= 5184

= 72

Now,

Perimeter of square = perimeter of rectangle

Side×4 = perimeter of rectangle

72×4 = 2 (l+b)

288 = 2 (2x+x)

288/2 = 3x

144/3 = x

x = 48

So, breadth = x = 48

and length = 2x = 2×48= 96

Therefore area of the field

= l × b

= 96×48

= 4608m^2

HOPE IT HELPS YOU

Plz mark as brainalist.

Answer 2

Solution :

Given,area of square field is 5184 m²

★ Area of square = (side)²

→ 5184 = (side)²

→ side = √5184

→ side = 72 m

Let's find the perimeter of the square field :

★ Perimeter of square = 4 × side

→ Perimeter = 4 × 72

→ Perimeter = 288 m

Let's move to the rectangular portion -

Let the breadth of rectangular field be x and length be 2x

★ Perimeter of rectangle = 2(l + b)

→ Perimeter = 2(2x + x)

→ Perimeter = 4x + 2x

→ Perimeter = 6x

Given, Perimeter of square field is equal to the perimeter of rectangular field.

→ 288 = 6x

→ x = $\sf\cancel\dfrac{288}{6}$

→ x = 48 m

• Breadth of rectangular field = 48 m

• Length of rectangular field = 48(2) = 96 m

Now, Let's find area of the rectangular field :

★ Area of rectangle = Length × Breadth

→ Area = 96 × 48

→ Area = 4608 m²

$\therefore$ Area of the rectangular field is 4608 m².