Question

The area of a square field is 841 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 :

• The area of a square field is 841 m².
• A rectangular field whose length is twice its breadth has its perimeter equal to the perimeter of the square field.

To find :

• The area of the rectangular field =?

Step-by-step explanation :

It is Given that,

The area of a square field is 841 m².

As We know that,

Area of square = side²

Substituting the values in the above formula, we get,

side² = 841

side = √841

side = 29.

Therefore, the side of square field = 29 cm.

Now,

As We know that,

Perimeter of square = 4 × side

Substituting the values in the above formula, we get,

= 4 × 29

= 116.

Therefore, Perimeter of the square field = 116 m.

As given in the above question,

Perimeter of the square field = Perimeter of the rectangle field = 116 m.

And,

A rectangular field whose length is twice its breadth.

Let, the breadth of the rectangle field be, x.

Then, the length of the rectangle field be, 2x.

As We know that,

Perimeter of the rectangle field = Perimeter of rectangle = 2(length + breadth)

Substituting the values in the above formula, we get,

➮ 2(2x + x) = 116

➮ 2 ( 3x ) = 116

➮ 6x = 116

➮ x = 116/6

➮ x = 58/3.

Therefore, We got the values of, x = 58/3.

Hence,

Breadth of the rectangular field, x = 58/3 m

Length of the rectangular field, 2x = 2(58/3) = 116/3 m

Now,

As We know that,

Area of Rectangle = length x breadth

Substituting the values in the above formula, we get,

= 58/3 × 116/3

= 6728/9

= 747.56

Therefore, Area of the rectangular field = 747.56 m².

Answer 2

$\sf{\underline{Answer\::}}$

Area of the rectangular field is 747.29 m²

$\sf{\underline{Explanation\::}}$

We have two fields, one of which is square in shape and the other is rectangular shaped.

The area of the square field is given to be 841 m².

Ahead the question gives certain Idea about the rectangular field.

About rectangular field,

• The length is twice it's breadth.
• Also, the perimeter of the rectangular field is equal to the perimeter of the square field.

We need to find the area of the rectangular field using these data.

Following the order of the question, let's intiate from the square field.

Let's suppose the side of the square field is x m.

Using the first statement,we know that we are supposed to use the formula for area of the square.

=> $\sf{Area\:of\: square\:=(Side)^2}$

=> $\sf{841\:=x^2}$

=> $\sf{x\:=\:\sqrt{841}}$

=> $\sf{x\:=29}$

The side measure of the square field having an area of 841 m² is 29 m.

Now,the question says about the length and breadth of the rectangular field.

So based on the statement of question,

• Length = 2x m
• Breadth = x m

Next,the perimeter of the square field is same as the perimeter of the rectangular field.

Here,we infer that we need to use formula based on perimeters.

$\sf{=>\: Perimeter\:of\: square\:=\: Perimeter\:of\: rectangle}$

$\sf{=>\:4\:(side)\:=\:2\:(length\:+\:breadth)}$

$\sf{=>\:4(29)=\:2(2x+x)}$

=> $\sf{\:116\:=2(3x)}$

=> $\sf{116\:=6x}$

=> $\sf{\dfrac{116}{6}\:x}$

=> $\sf{19.33\:=x}$

So,the breadth of the rectangle is 19.33 m.

We know that the length of the rectangle is twice the breadth.

So,

• Length = 2(19.3) = 38.66 m

We now have the dimensions of the rectangular field. Substituting these value in the formula of area of the rectangle to solve for the area of the rectangular field would be the last and simplest step.

It is known that the area of the rectangle is,

• Length × Breadth

=> $\sf{Area\:=\: Length\:\times\:Breadth}$

=> $\sf{Area\:= 38.66\:m\:\times\:19.33\:m}$

=> $\sf{Area\:=747.29\:m^2}$