Question

3. Area of a square field is 3600m2. A rectangular field whose length is twice its width has
perimeter equal to perimeter of square field. Find the area rectangular field. (3200m)​

Answer 1

Answer:

3200m2

Step-by-step explanation:

Area of square field=3600m2

Area of a aquare = a2 where a is the side

a2=3600

a=√3600

a=60m

Hence one side of the square field is 60m

Perimeter of square=4a

                                =4*60

                                =240m

Let the length of the rectangle be 2x

Then the breadth of the rectangle is x

Perimeter of rectangle=2(lenght+breadth)

Also given that primeter of rectangle is equal to the perimeter of square

2(x+2x)=240

2(3x)=240

6x=240

x=240/6

x=40m

hence lenght=2x=2*40=80

breadth=x=40

Area of rectangle = lenght * breadth

                             = 80*40

                             =3200m2

Answer 2

Given :

• Area of the square field is 3600 m².
• A rectangular field whose length is twice its width has perimeter equal to perimeter of square field.

To find :

• Area of the rectangular field.

Solution :

• Area of the square field = 3600 m²

A/Q,

side² = 3600

→ side = 60

Therefore,

• Perimeter of the square = 4×60 = 240 m

Consider,

• Length of the rectangular field = x m
• Width of the rectangular field = y m

According to the 1st condition :-

• A rectangular field whose length is twice its width.

$\implies\sf{x=2y..............eq[1]}$

According to the 2nd condition :-

• A rectangular field whose length is twice its width has perimeter equal to perimeter of square field.

$\implies\sf{2(x+y) = 240}$

$\implies\sf{2y+y)=120\:[put\:x=2y\: from\:eq(1)]}$

$\implies\sf{3y=120}$

$\implies\sf{y=40}$

• Width of the rectangular field = 40 m.

Now put y=40 in eq[1]

$\implies\sf{x=2y}$

$\implies\sf{x=2\times\:40}$

$\implies\sf{x=80}$

Area of the rectangular field = 80×40 m²

→ Area of the rectangular field = 3200 m²

Therefore, the area of the rectangular field is 3200 m².