Question

the area of a square field is 5184 m2. 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.

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 ✝

_______________________

Answer 2

Given :-

Area = 5184 m

Length is twice of breadth

To Find :-

Area

Solution :-

Let the side of square be x

$\sf 5184 = x \times x$

$\sf 5184= x^2$

$\sf \sqrt{5184} = x$

$\sf 72 = x$

Now

Perimeter of square =4s

Perimeter = 4(72)

Perimeter = 288 m

Now

Let length be 2x and breadth be x

288 = 2(2x + x)

288/2 = 2x + x

144 = 3x

144/3 = x

48 = m

Hence

Breadth = 48 m

Length = 2(48) = 96 m

Area = lb.

$\sf Area = 96 \times 48$

$\tt \: Area = 4608 \; m^2$