Question

The area of a square field is 5184 m . 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

First step: find the side of square and perimeter

Second step: comparing perimeter of square and rectangular field because given- perimeter of rectangular field =perimeter of square

find the length and breath for help perimeter of rectangular field

and last find the area of field

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 ✝