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:

Given :

i) Area of a square field(A1) = 3600m²

ii) Length of rectangle(l2) =2× breadth of rectangle (b2) l2 = 2 × b2

iii)Perimeter of rectangle(P2) = perimeter of square(P1)

To find : Area of rectangular field(A2)=?

Solution:

Area of a square field(A1) = 3600m²

(l1)²=3600m²

l1 = 60 m.....(1)

Perimeter of square (P1) = l1 ×4

=60×4

=240m........(2)

Thus,

Perimeter of rectangle(P2)=240m....(3)

Perimeter of rectangle(P2)= 2(l2+b2)

= 2(2b2+b2)

= 2(3b2)

=6b2

240=6b2

b2=40m.....(4)

l2 = 2×b2

= 2 ×40

=80 m.....(5)

Area of rectangular field = l2 × b2

= 80m × 40m

= 3200m².

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Answer 2

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• 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.

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• What's the area of the rectangular field?

Formula to be used :-

• Area of a square = a²

Where,

a = side

• Perimeter of a square = 4a

• Area of a rectangle = Width × Breadth

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

As per question :-

Given that,

Area of the square field = 3600 m²

Hence,

⟹ a² = 3600

⟹ a = 60

Then,

perimeter of the square filed

= 4a

= 4 × 60

= 240 m

________________________________________________

Let the length and breadth of the rectangular field be x m and y m respectively.

Given that,

A rectangular field whose length is twice its width.

Hence,

⟹ x = 2y.............. eq(1)

Again, it’s given that

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

Therefore,

⟹ 2 ( x + y) = 240

⟹ x + y = 120............ eq(2)

Put x = 2y in eq(2)

⟹ x + y = 120

⟹ 2y + y = 120

⟹ 3y = 120

⟹ y = 40

Substituting y = 40 in eq(1)

x = 2y

⟹ x = 2 × 40

⟹ x = 80

Hence,

Width of the rectangular field is = 40 m

Breadth of the rectangular field is = 80 m

Therefore, area of the rectangular field is

= Width × Breadth

= 80 × 40

= 3200 m²

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