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

Area of square=841 m^2

side × side = 841

side = 29 m

Perimeter of square = 29 × 4 m

= 116 m

Let the breadth of the rectangle be x m.

Length = 2x m.

Perimeter = 2(x+2x) m

= 2(3x) m

= 6x m

Perimeter of square = Perimeter of rectangle

116 = 6x

x = 116/6 m

x = 58/3 m

Area of rectangle = length × breadth

= 2x × x

= 2x^2

= 2×(58/3)^2

= 6729/9 m^2

= 747.56 m^2

If the calculation is correct then this is the required answer.

Answer 2

Answer:

The area of rectangular field : 747.56 m².

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 rectangular field.

Solution:

We are 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.

We know,

◉ Area of square = ( Side )²

➞ 841 = ( Side )²

➞ Side = √841

➞ Side = 29 m.

◉ Perimeter of square : 4 × Side

Perimeter of square : 4 × 29

Perimeter of square : 116 m.

but According to given condition,

Perimeter of square = perimeter of rectangle

but ,

◉perimeter of rectangle = 2 ( length + Breadth)

Let the length and width of the rectangle be l and b.

➨116 = 2 ( 2b + b ) ............. ( 1 )

according to second condition,

➨l = 2( b )

put value of l in equation ( 1 )

➵116 = 2 ( 2b + b )

➵116 = 6b

➵b = 116 / 6

➵b = 58 / 3

therefore , l = 2 × 58 / 3

l = 116 / 3 m.

Now,

◉ Area of rectangle = length × breadth

➵Area of rectangle = ( 116/3 ) × ( 58/3 )

➵Area of rectangle = 6728 / 9

➵Area of rectangle = 747.56 m².

Therefore, The area of rectangular field is 747.56 m².