Question

the area of a square field is 5184 metre square or rectangle field whose length is twice the breadth has its perimeter is equal to the perimeter of the square field find the area of the rectangular field ​

Answer 1

Answer:given,

the area of square is=5184m²

s×s=5184

s²=5184

s=√5184

s=72

according to problem,

l=2x

b=x

we know that,

perimeter of square=perimeter of rectangle

4s=2(l+b)

4×72=2(2x+x)

288=6x

x=288/6

x=48

from problem,

l=2x

=2×48

=96

b=x

=48

therefore length is 96

              breadth is 48

area of rectangle = l × b

                           = 96 × 48

                            =4608 m²

Answer 2

Given:-

• ↦ Area of square field = 5184 m².

To Find:-

• ↦ Area of rectangle.

Formula to be used:-

• ↦ Perimeter of square = 4a

• ↦ Perimeter of rectangle = 2 (l + b)

Solution:-

• ↦ Let the side of square field as a.

Then,

• ⇒ a² = 5184 m²
• ⇒ a = √5184 m
• ⇒ a = 2 × 2 × 2 × 9 = 72 m

Now,

• ↦ Perimeter of square = 4a
• ↦ Perimeter of square = 4(72)
• ↦ Perimeter of square = 288 m

Now,

Perimeter of rectangle = 2 (l + b)

• ⇒ 288 = 2 (l + b)

As length is twice of its breadth,

• ⇒ 288 = 2 × (2b + b)
• ⇒ 288 = 2 × 3b
• ⇒ 288/2 = 3b
• ⇒ 144 = 3b
• ⇒ 144/3 = b
• ⇒ b = 48

Here, breadth is 48 m

Now length,

• ↦ Length = 2 × 48 = 96 m

Now, Area of rectangle  ;

• ↦ Area of rectangle = l × b

• ↦ Area of rectangle = 96 × 48

• ↦ Area of rectangle = 4608 m².

✝ Hence, the Area of rectangle is 4608 m² ✝

_______________________