Question

The area of a square field is 3249 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 the square field : 3249m²

Length of the rectangle is twice it's breadth.

The perimeter of square and rectangle are same.

To find :

The area of the rectangular field.

Solution :

First, we should find the side of the square.

Side of a square :

$\sf \dashrightarrow Side \times Side = Area$

$\sf \dashrightarrow x \times x = 3249$

$\sf \dashrightarrow {x}^{2} = 3249$

$\sf \dashrightarrow x = \sqrt{3249}$

$\sf \dashrightarrow x = 57$

Now, we should find the perimeter of the square.

Perimeter of the square :

$\sf \dashrightarrow 4 \times Side = Perimetre$

$\sf \dashrightarrow 4 \times 57$

$\sf \dashrightarrow 228 \: metres$

We know that, the Perimetre of the square is same as the Perimetre of the rectangle. So, let's find the values of length and breadth by the formula of perimetre of rectangle.

Let the breadth be y.

Let the length be 2y.

Breadth of the rectangle :

$\sf \dashrightarrow {Perimetre}_{(Rectangle)} = 2 \: (Length + Breadth)$

$\sf \dashrightarrow 228 = 2 \: (2y + y)$

$\sf \dashrightarrow 228 = 2 \: (3y)$

$\sf \dashrightarrow 2 \: (3y) = 228$

$\sf \dashrightarrow 3y = \dfrac{228}{2}$

$\sf \dashrightarrow 3y = 114$

$\sf \dashrightarrow y = \dfrac{114}{3}$

$\sf \dashrightarrow y = 38$

Length of the rectangle :

$\sf \dashrightarrow 2y = 2(38)$

$\sf \dashrightarrow 76 \: metres$

Now, we can find the area of the rectangle.

Area of the rectangle :

$\sf \dashrightarrow Length \times Breadth$

$\sf \dashrightarrow 76 \times 38$

$\sf \dashrightarrow {2888 \: metres}^{2}$

Hence, the area of the rectangular field is 2888 metres².

Answer 2

Answer:

Given :

Area of the square field : 3249m²

Length of the rectangle is twice it's breadth.  

The perimeter of square and rectangle are same.  

To find :

The area of the rectangular field.  

Solution :

First, we should find the side of the square.  

Side of a square :        

 Now, we should find the perimeter of the square.  

Perimeter of the square :  

We know that, the Perimetre of the square is same as the Perimetre of the rectangle. So, let's find the values of length and breadth by the formula of perimetre of rectangle.

Let the breadth be y.

Let the length be 2y.  

Breadth of the rectangle :    

Length of the rectangle :

Now, we can find the area of the rectangle.

Area of the rectangle :

Hence, the area of the rectangular field is 2888 metres²

Step-by-step explanation:

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