Question

The area of a square field is 5184 m². 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

Answer

The area of the rectangular field = 4608m².

Step-by-step explanation:

To Find :-

• The area of rectangular field.

★ Solution

Given that,

• The area of square field = 5184m²
• Perimeter of square field = Perimeter of Rectangular field.
• The length is twice the breadth.

First, finding the side of square field :-

⇒ (side)² = Area of square

⇒ (side)² = 5184

⇒ side = √5184

⇒ side = 72m

Now, perimeter of the square field :-

⇒ 4 × side = Perimeter of square

⇒ 4 × 72

⇒ 288m

As given per question,

Perimeter of Rectangular field = Perimeter of square field = 288m

Finding the length and breadth of rectangular field :-

Let us assume the length and breadth of the field (Rectangular) as 2x and x respectively.

⇒ 2 ( length + breadth ) = Perimeter

⇒ 2 (2x + x) = 288

⇒ 2x + x = 288/2

⇒ 2x + x = 144

⇒ 3x = 144

⇒ x = 144/3

⇒ x = 48

The value of x is 48.

∴ The length and breadth is :-

• Length = 2x = 2*48 = 96m
• Breadth = x = 48m

Now, According the question,

• The area of Rectangular field :-

We know,

Area of rectangle = length × breadth,

Therefore,

⇒ length × breadth

⇒ 96m × 48m

⇒ 4608m²

Hence, The area of the rectangular field is 4608m².