Question

The area of a square field is 5184 metre square. a recrangular field whose length is twice its breadth, has its perimetre equal to the perimetre of a square field. find the area of a square field.​

Answer 1

Answer: 4608 m²

Step by step explanation:

Area of the square field is 5184 m².

Therefore, Side= √5184 m = 72 m.

Finding it's perimeter,

= 4 × Side

= 4 × 72

= 288 m.

Now, ATQ,

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

Given that,

Perimeter of rectangular field = Perimeter of square field.

.°. Perimeter of rectangular field = 2 [ length + breadth ] = 288 m.

2 [ 2x + x ] = 288

2 × 3x = 288

6x = 288

x = 48 m

Thus, Breadth = 48 metres.

Length = 2x = 2 × 48 = 96 metres.

Now, We've got the value of both length and breadth.

To find: Area of square field.

Area of square field= Length × Breadth.

= 96 × 48

= 4608 m²

Therefore, The area of square field is 4608 m².

Answer 2

Correct Question :

The area of a square field is 5184 metre square. a rectangular field whose length is twice its breadth, has its perimetre equal to the perimetre of a square field. find the area of the rectangular field.

______________________________

Given :

• Area of square field = 5184 m².
• The length of the rectangular field is twice of its breadth .
• Perimeter of square field = Perimeter of rectangular field .

To Find :

• Area of the rectangular field .

Solution :

Area of square field = 5184 m²

→ (Side)² = 5184 m²

→ Side = √5184 m²

→ Side = 72 m

The side of the square field is 72 m

Now,

Let the breadth of rectangular field be x

then the length will become 2x

Perimeter of square field = Perimeter of rectangular field

→ 4 × Side = 2( L + B )

→ 4 × 72 = 2( 2x + x )

→ 288 = 2 × 3x

→ 288 = 6x

$\rightarrow \sf{ \dfrac{288}{6} = x }$

→ x = 48 m

So, Breadth of the rectangular field is 48 m

→ 2 × 48 m

→ 96 m

And, length of the rectangular field is 96 m

Area of rectangular field = Length × Breadth

→ 48 m × 96 m

→ 4608 m²

$\qquad \underline{ \fbox{ \sf{Area \: of \: rectangular \: field \: is \: 4608 m^{2}}}}$