Question

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The area of a square field is 5184 m². Find the area of a rectangular field, whose perim
is equal to the perimeter of the square field and whose length is twice of its breadth.​

Answer 1

Area of square field = 5184 m²

Side of square = √5184 = 72 m²

Perimeter of square = 4 × side

= 4 × 72

= 288 m

↦ Perimeter of rectangular field = Perimeter of square (Given)

↦ Length of rectangular field = 2B (b = breadth of rectangular field)

↦2 (2b + b) = 288

↦2 (3b) = 288

↦ 3b = 144

↦ b = 48 m

↦ So, length = 2b = 2×48 = 96 m

Now, Area of field = l × b

= 96 × 48

= 4608 sq. m

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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