Question

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

Answer 1

Given :

• Area of square field = 5184 m² .
• Length of rectangular field = 2 (breadth)
• Perimeter of rectangle = Perimeter of square

To find :

• Area of rectangular field

Solution :

Area of square field = side²

5184 = side²

Side = √5184

Side = 72 m.

Perimeter of square = 4 × side

= 4 × 72

=288 m

Perimeter of rectangle = Perimeter of square

2 (length + breadth) = 288

2 ( 2b + b) = 288

2(3b) = 288

6b = 288

b = 288/6

breadth = 48

Length = 2 × breadth

= 2 × 48

= 96 m

Area of rectangular field = length × breadth

= 96 × 48

= 4608 m²

$\underline{\sf \therefore The\ area\ of\ rectangular\ field\ is\ 4608\ m^2}$

Answer 2

Given:-

• ↦ Area of square field = 5184 m².

To Find:-

• ↦ Area of rectangle.

Formula to be used:-

• ↦ Perimeter of square = 4a

• ↦ Perimeter of rectangle = 2 (l + b)

Solution:-

• ↦ Let the side of square field as a.

Then,

• ⇒ a² = 5184 m²
• ⇒ a = √5184 m
• ⇒ a = 2 × 2 × 2 × 9 = 72 m

Now,

• ↦ Perimeter of square = 4a
• ↦ Perimeter of square = 4(72)
• ↦ Perimeter of square = 288 m

Now,

Perimeter of rectangle = 2 (l + b)

• ⇒ 288 = 2 (l + b)

As length is twice of its breadth,

• ⇒ 288 = 2 × (2b + b)
• ⇒ 288 = 2 × 3b
• ⇒ 288/2 = 3b
• ⇒ 144 = 3b
• ⇒ 144/3 = b
• ⇒ b = 48

Here, breadth is 48 m

Now length,

• ↦ Length = 2 × 48 = 96 m

Now, Area of rectangle  ;

• ↦ Area of rectangle = l × b

• ↦ Area of rectangle = 96 × 48

• ↦ Area of rectangle = 4608 m².

✝ Hence, the Area of rectangle is 4608 m² ✝

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